This character would be a half Russian half American, raised in the US as a special ops soldier and is fighting on a mission in the Bosnian War that was in 1995. He meets a woman who's either of Bosniak or Serbian descent and has a kid. What would be the consequences in doing this? Would it make a difference?
Could you call the military base and ask them? That would seem to be the best way to get the answer to this question. The only similar plot I have seen is in the Lee Child Jack Reacher story, "Never Go Back" where it is implied he had an affair with a civilian while posted overseas and she made a claim for child support against him. He (Jack Reacher) didn't know anything about it until he visited a military base and was arrested. My gut reaction, with *no* knowledge is that the kid could have a claim on the dad's money, perhaps a claim for citizenship, and he could face bullying from his peers within his ethnic group for having an American father....? My guesses anyways.