If a father abandons his children but later threatens to fight for sole custody due to a child support claim being filed, will he get it?

Question Details:

I have 2 children, by the same man. The father signed the birth certificate for our oldest son but not our youngest. When I was in my third trimester with our youngest son, the father abandoned us. He impregnated his new girlfriend within a month of them meeting. He didn't make any contact with me or our sons from 11/09 until 10/10. In October, he met our youngest son and visited with both kids a handful of times before he left again. I have tried getting him to visit all the time but he never does. Now that I filed for child support, he is threatening to fight for partial custody. He has helped out with no more than $200 in the last 2+ years, my kids have no clue who he is. I work 2 jobs and attend college to support them. I've done everything for them by myself. They are in day care 5 days a week from 6:30 am until 4 pm as I work 7 am - 3 pm daily. Is there any chance that he can get partial custody as he has abandoned them for almost their whole lives?

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