Which pair of limbs should the wings be attached to for this bio-engineered creature? (A or B) The creature itself does not have a set weight and is built to fight other similarly sized creatures. It is wyvern/alligator like with a very low stance and will need to use its wings to shield from attacks when necessary and it’s wings should be as out of the way as possible for the most part for more mobility. It’s flight pattern is mainly soaring with occasional quick bursts of speed. TLDR, is A or B the best limb for wing attachments for flight in the most efficient possible way?
As it is right now, probably B, but only because "C" is not an option.
warning: ramblings about long tails and pterosaurs ahead
Since you're asking about optimal wing placement, I'll start off by saying one thing: the lighter and smaller your bioengineered Wyvern, the more plausible it will be as it currently is in terms of overall proportions and stance. The lizard like splayed posture is much more sustainable in a smaller animal where the limbs don't have to carry as much weight thanks to our good old frenemy the square cube law.
That said, we're talking wyverns and lizards with membranous wings, and they aren't bipedal, so that means a prime opportunity to talk about the closest example we know of: pterosaurs:
The skeleton above belongs to a dimorphodon, which funnily enough is a very close analog for what we want here. As far as current research seems to go, Dimorphodon was not a fish eating pterosaur, nor was it a prime example of a graceful flier. This pterosaur apparently had very well developed limbs and was likely very skilled at moving on the ground, being able to run and climb after its prey, which it dispatched using its large jaws. It mainly hunted creatures smaller than itself though.
There's just a tiny problem: dimorphodon itself was fairly tiny.
You see, pterosaurs with long tails were often small, and even then their tails were bony and inflexible in general as to remain light. Your creature has an extremely flexible and therefore muscular tail, and it is about twice as long as the thing itself. That wouldn't be a problem if the goal wasn't for this to fly. Usually you want the creature's center of mass to be kept very close to the wings, but with that tail even putting the wings on the rear legs might still not be enough to get them in that point. Flexible and heavy tails are also bad for a flying creature because it takes a lot of energy just to keep them from flopping around and messing with balance, especially when compared to a stiff tail or no tail.
To give you a better idea of what it takes for a really large creature to fly in the real world, here's one of the largest flying apex predators known to man: Hatzegopteryx.
This is also an incredible example for our case because it is probably THE BEST real life example we have of what you want: this guy probably weighted around 250 kg or a quarter of a ton. Because of how large and heavy it was, it was mostly adapted to living on the ground and could likely run at decent speeds, but was a skilled flier regardless of that. Due to living mostly on the ground and on an island, its wings could probably fold tightly against it's body to minimize damage (and speaking of damage: using wings as a shield to block attacks is a terrible idea. They're better off used to escape into the air so that you don't have to deal with further damage 9 times out of 10). It's neck and Jaws were also sturdier than those of similarly sized pterosaurs, meaning they could hunt things of similar size to themselves (which is quite a feat for something that was taller than a T-Rex but weighted at least twenty times less).
Basically, these guys ruled their habitat as top dogs, relied mostly on soaring while still being able to fly fast and cover huge distances, and were well adapted at moving on the ground with minimal interference from their wings. Rather than lizards, these guys were built more like storks, but their long necks were far from the most flexible. Their strange appearance however isn't just for show, nearly every tiny anatomical trait in these guys was there to ensure they could remain able to fly despite growing so large.
So as it is, despite looking extremely cool, your creature is not structured to do what you want it to. if we're being realistic, neither A nor B would cut it, and the last pair would probably still not be enough. You'd be better off just attaching a membrane to its limbs and tail and make it only capable of gliding, and chances are the tail would still get in the way. The only way I see the tail being less of a problem would be if it could flatten up like the body of a flying snake, and even then it'd probably only be enough for the animal to glide.
If However we start to value function over form and coolness, that doesn't cut it. If the we're strictly asking for something that's mobile, durable and airborne, then removing the tail is the best way to go. Assuming you want this to be good at running and climbing and able to fly based on your design and what you said, removing the tail alone makes it significantly lighter and thus better at taking off. The creature already has 6 limbs, so a tail does little for climbing. If the tail is meant as a long ranged weapon, lengthening the neck and strengthening the jaw results in a lighter, nature-approved alternative that's highly effective. This holds true even if the creature is smaller and light enough to be technically able to fly, because it means we the tail's bone and muscle mass can be redistributed around other parts of the body for a more durable creature.
As goofy as it might look, Hatzegopteryx is quite literally what peak performance for a large flying apex predator looks like, and it makes sense given how advantageous the ability to fly is, and if you want your animal to be agile and able to fly while also being large, you'd do well to look at azhdarchid pterosaurs, herons and secretary birds. For it to keep the lizard like proportions and longer tail, it'd realistically need to be smaller since it's proportionally stronger and tougher (though it's likely it'd be a clumsy flier), but a larger animal will need to have a less splayed limb posture and sacrifice a lot more towards flight, as it literally becomes exponentially harder for something to fly the bigger it gets.
Without changing the design (because let's face it, it's a bloody cool design, props to your drawing skills) and ignoring the annoying details, B is still the most plausible as it brings the wings a bit back and closer to the creature's center of mass. It's also better for believability if the wings are not used as shields against anything physical unless it's small enough to be harmless, and just making the wings fold tightly against the limb should already be enough for it to be out of the way regardless of whether it's on A or B.
If we're actually striving for a more realistic creature, it would benefit from looking less like a lizard and more like a heron, with a longer neck and basically nonexistent tail. In this scenario, A becomes the better option since the longer neck and potentially head brings the center of mass closer to the front of the creature. Again the wings should be kept as a means of transportation only and being used for defense only as a way to intimidate foes at best, and should remain tightly folded against the body so they're not damaged while it's fighting, running or climbing around, because the ability to fly in itself is already one of the best counters against melee attacks.
I don't know what you mean by "most efficient." That's phrase that pops up on Worldbuilding frequently, but it's entirely subjective. Unless you explain what you mean by "efficient" (or, more specifically, what variables are in play when considering efficiency), then we must make assumptions about what you mean. Here's an example:
I declare "most efficient" to mean "least amount of energy needed to sustain long-term flight"
My definition of "most efficient" means the mass of the creature must be balanced front-to-back. The weight of the base of the tail, which appears to have no value to flight other than to allow weight to be shifted for turning purposes (e.g., there are no feathers, so it can't be used as a rudder or significantly as an elevator). But, like bats, it can serve as a stabilizing force.
But, based on the pictures, it will have significant mass (note that most bats have almost trivial tails... every ounce of tail requires energy to lift without contributing substantial value to flight).
To that end, "most efficient" (in terms of long-term sustained flight) places the wings over the rear haunches or between the two rear pairs of limbs, thereby distributing the weight and minimizing the amount of force needed to keep the creature level.
It's worth remembering that, generally, when it comes to natural flight, evolution made everything as light and evenly distributed as it could. Narrow tails, hollow bones, etc. The fundamental problem with trying to find a "realistic" or "scientifically supported" (my quotes) placement of wings on a lizard is that pretty much nothing about a lizard supports flight. From that perspective, "most efficient" means "most efficient for your story," which is a question we don't answer on this Stack.