What can I do if my husband abadons my children?

In which state is he filing?

Custody cases such as yours are complicated. I can't provide you with a sufficient answer without more information. And, my responses will only be applicable to Washington State.

Your question doesn't make it clear whether you have both a husband and a boyfriend, so it isn't clear who is trying to do something. Nor is it clear whether he is trying to do it in Maryland or Florida. But, basically it doesn't appear that anything can be done in Maryland because you and the children are not living there and apparently never did live there. If you have lived in Florida for more than 6 months and there has never been any kind of custody case affecting the children somewhere else, custody decisions can only be made in Florida. If it has been less than 6 months since you left Indiana, Indiana courts are where any new custody decision needs to be made. If you want to obtain child support, your options are to wait until he starts a legal case in Florida or go to your local child support enforcement office to have them start a child support action that will have to be transferred to Maryland. The question is not whether he "can get custody" because if he is the father he clearly "can". The real question is "will he succeed" if he actually goes to court somewhere and the answer to that is totally based on what is in the children's best interest. Only an attorney with the opportunity to evaluate all the relevant facts can give you some estimate of what might happen in a court.

Yes, under some circumstances he can end up the custodial parent. Take this issue seriously and see a domestic relations attorney soon to discuss your options and the specifics of this case.

You put him in jail for non-support and if he files for custody you get a lawyer.