I just got divorced here in KY and my understanding is that joint custody is most often awarded, meaning both parents have equal rights to decisions regarding the raising of the children (school, healthcare, religion, etc.), with one parent (most often the mother), as the custodial parent, meaning the children live primarily with that parent & have regular visitation with the non-custodial parent. I think most states generally give the mother custodial rights, as long as she's not deemed unfit; however, many states are making an effort to be more equitable as far as the father's rights for custody are concerned. In some cases, 50/50 custody will be granted (parents share time with the child equally), if one parent wants that and the other does not fight it.
Is your ex trying to get full custody of your child (meaning he wants sole custody as we as sole responsibility)?? I can't imagine that a court in any state would give either parent sole custody as long as both are considered to be fit parents. Or does he just want to be the custodial parent, meaning your child will live with him & have regular visitation with you? I suppose that could happen, but I think if you are a fit parent & you fight that, most likely you would either win or at least get 50/50 custody. I'm not a lawyer & don't know your state laws but that's my general understanding of how things work in most places.
My divorce took about 3 months once my ex finally got a lawyer, but we had no custody issues. I wish you the best of luck...I know how frustrating & emotional the process can be.