I need medical assistance etc. because I am a single mom. I don't want any support from the "dad" because he is not on the birth certificate, is verbally abusive...
I have been told I have to give all and any info I have on him so they can go after him for support. He has other kids he doesn't support, no job and a felon.
How do I protect myself and my child? Do I Have to give the info about him I do know?

...i have been told i have to give all and any info i have on him so they can go after him for support.... Do i Have to give the info about him i do know?

These statements are inconsistent.

Do you think the social workers are lying to you?

There are many jurisdictions with varying regulations/laws you could be posting from. Any experts reading your inquiry wouldn't know which set applies to your situation.

Do you seriously think your application will be accepted if you don't supply the information they ask for?

The agency you are applying to is probably obligated to seek as much of its client aid funding as possible from the two parents that produced the child. The taxpayers supplying the other funds have obligations of their own and aren't inclined to allow your former lover to neglect his obligations. In some jurisdictions an absentee parent will be required to send support payments to the government instead of directly to the custodial parent.