So lets examine this
You have a need to "freeze" something in time. Almost certainly a person - you eliminate the "indestructible" element as a mandatory criteria therefore you are not trying to bring undamaged through time some inanimate object.
You also are looking fo a stasis "beam" - looks like you are after some kind of possibly portable device/ weapon that can send a person into stasis unexpectedly and against their will.
I would have such a device be created probably with the use of some exotic mineral/ element. I would have this arrive/ be discovered through either being on/in a meteor OR by being alien tech. The alien tech is a bit of an easy cop-out in terms of science - because it doesn't really need to be explained.
On/In a meteor is a bit tougher - and therefore would take a bit of space in your story. You will have to put in a bit of time describing the discovery of some new mineral/ element/ compound with unimaginable properties on a recent meteor. Somebody discovering it. Then having the smarts to do something with it - and then develop the device into some kind of portable "weapon". This really only works well if you have a Tony Stark like figure to whip something up.
Effectively - I would have your science genius obtain the meteor and mess about with it a bit. I would have them very quickly spot there is something odd about the material it is made of - then start in with some nondestructive tests. Probably some kind of X-Ray. I would then have them notice something odd as a result.
The odd thing they would notice could simply be some strange fluorescing as they attempt to x-ray. And no exposure on the X-Ray film. They would then try other substances other than the X-Ray film - including bacteria on a petri dish. While it doesn't kill the bacteria - they notice it doesn't multiply either - which is a bit atypical for bacteria. After some further experiments - they eventually decide to try it on a mouse. BINGO - they find out they have created a stasis beam. With a bit of work they figure out that one frequency causes stasis - and a different part of the spectrum causes stasis to be cancelled.
They would then turn the Meteor material into a lens - hook up some kind of portable x-ray generation and VOILA - you have your Stasis Beam.
An obvious risk would be sending only part of a person/ creature into stasis. Another risk would be if somebody else was standing on the other side of your intended target.
One possible Scientific basis for this is it affects materials through an immediate stopping of ALL vibration/ energy usage - therefore essentially "freezing" the target in place.
Hopefully this gives you some simple & usable basis for developing this tech!