This is interesting.
Since your stepson lives with you more than 50% of the time, for FAFSA purposes, you only need to include your and your wife's financial information - not his biological father's.
However, there does seem to be some conflicting information here. You mention that your son's biological father claims him on his taxes, yet he lives with you more than 50% of the time. According to tax laws, you may only claim a dependent who lives with you more than half time, so it would seem that the father is ineligible to claim the son as a dependent child.
For help, you may want to consult a financial advisor or talk with the school's financial aid office - being claimed inaccurately on a tax form may affect the FAFSA, so I'd suggest calling the school's financial aid office to learn more.