I missed that your post said it is 50/50 custody, which complicates things significantly. Unfortunately, I can't give you any definite, but here are some thoughts:
First, there is no such thing as 50/50 custody for tax purposes (and Medicaid purposes). Who does the child live with more nights during the year? That is the "custodial parent".
From a strictly literal viewpoint, the Federal rules seem to indicate that BOTH of your incomes may be used to determine Medicaid eligibility. It says "if living with the individual" ... then "the individual's parents" income is included. To me, that seems to indicate both of your incomes should be included.
However, the prior paragraphs in the law hint that it would be the "custodial parent" is who considered to "live with the [child]". From what I have seen and heard, that is consistent with most Medicaid application forms. So *IF* you are the "custodial parent", that would mean only your income would be counted, regardless if your ex claims the child.
I'm sorry I can't give you anything more definite. I think you may just need to fill out the Medicaid applications honestly and hope for the best.
