I am a step mother of two children I have been caring for the for 2 years now the biological mother lives in another state and gave the kids to my husband they biological father because she no longer wanted her kids nor to care for them anymore she hasn't seen them or talked to them in these two years my husband is now in prison for the last year and I have been caring for them by myself while he has been incarcerated I am currently on cal works receiving aid and my step children are on my case so I'm trying to find out if I can file for child support against the biological mother by myself?

Your husband can file for support and can have that support paid to you.

The issue here is, that you have no legal rights to even have the kids in your care and custody.
I am glad you are there and willing to do this, but legally you can't get them medical care, can't enroll them in school or anything, I am sure they are letting you, but legally this can be a issue.

You have no standing at all to file for support.

I'm also concerned about the statement that the mother "gave the kids to my husband". Kids are not property that can be given (well kids (baby goats) are, but children aren't). The mother may have ceded custody to their father, hopefully that was done legally through the courts.

If your husband has legal custody, then he may be able to give you a limited power of attorney to make decisions for the children about medical care and schooling.