Nuclear fission rocket is becoming obsolete and is superseded by the more efficient antimatter engine, in fact there will be no pollution and the efficiency is around 100%.
Firstly, you can you create your antimatter. The pesky law of conservation of baryon number means that in most cases your maximum efficiency of antimatter creation will be 50%, because for every antiparticle your energy-to-mass system coughs up, you'll also get a corresponding normal particle. In practice, even a 1% efficiency would be astonishingly high. You'll need a vast and expensive infrastructure for antimatter synthesis.
Secondly, a 100% efficient conversion of energy release from annihilation into kinetic energy of exhaust products is basically impractical, and not just becasue thermodynamics hates you. About 33% of the annihilation energy will be in the form of neutral pions which will almost immediately decay into highly penetrating gamma rays. It will be Quite Difficult in most designs of antimatter engine to absorb those gamma rays into your reaction mass and have a high thrust engine, and in any design it will be impossible to both absorb all the gamma rays and have a high specific impulse (roughly: fuel economy). You'll get at most ~80% efficiency for a solid core antimatter engine, which will have a performance and Isp equivalent to a solid core nuclear rocket.
Thirdly, whilst your antimatter engine is running it will be kicking out, at a minimum, a lot of gamma rays. More complex designs with higher exhaust velocity will also spit out various kinds of interesting and unstable light particles which will themselves cause some issues but also eventually decay to gamma rays. Once the engine is turned off there will be a lot less residual radiation, but there will be some. A single antiparticle hitting a large nucleus (such as the tungsten core of a solid core antimatter rocket) will not annihilate the entire atom, but will transmute it and maybe even fission it. The resulting nuclides are not guaranteed to be stable!
It is at least a lot more plausible (and an awful lot safer) to use a solid-core antimatter rocket to lift off from Earth than to use a nuclear rocket of any kind. You need so little antimatter for the job that even a worse-case catastrophic accident will be quite non-destructive and there will be no fallout to be concerned about.
I'm wondering if in a space battle that takes place within the solar system is there any place for nuclear powered spaceship or they belong in space museums?
Nuclear rockets are a lot less versatile... not only are they more hazardous to maintain, but they can't be trivially turned on and off at will. This is fine for civilian purposes (where you will do be doing a couple of orbital injection burns at the start and end of your journey), or if you are making a torpedo, but it is slightly more inconvenient for a warship.
Their fuel on the other hand is almost certainly cheaper to obtain and simpler to store and a lot safer to be around once high-power weaponry starts going off in the neighbourhood.
The efficiency of antimatter is slightly less than you might think. It is up to you to determine the relative availability of antimatter vs fission fuel, which will ultimately tip the balance in favour of whichever outcome is best for your story, and we can't determine that for you!