Since he doesn’t live with you his father must give you a signed form 8332 giving you permission to claim him. I assume that you didn’t live with the dad any part of the last 6 months of the year in which you intend to claim him. You can’t get earned income credit based on claiming the dependency or child care credit and can’t use the child to qualify you to file as head of household.
https://www.irs.gov/pub/irs-pdf/f8332.pdf
