I'll rephrase my question, Is there a way to find out who's collecting my father's SS benefits other than my mother?

Are you sure they are collecting? SS is not an automatic thing. The mother would have to apply for it and have proof, birth certificate, that the he is the father.

Just a question, was your Dad married to ur Mom at time of passing?

It may be a shot in the dark, but consider one of those DNA testing kits, like the ancestry one. Assuming you give them permission to "share" your results and your potential half-siblings do the same, they may be able to match you up. A friend of mine did this and found out that the man who was his father was not his biological father when they connected his DNA profile to the profiles of people who turned out to be half-siblings.

I’m assuming your father has died and there’s some sort of other family, really any contact to a minor - imo - needs to be done either through their mother (to the minor) or done by the probate atty handling your fathers estate. You should not diy this.

SSA has very specific & narrow rules as to how children of SS recipients can get a $ benefit based on a parents SS history. It’s in SSA - POMS: RS 00203.001 child benefit provisions. SSA cannot - again CANNOT- share that information with you.

If there’s kids - from a non marriage- drawing on his SS, he would have done an some sort of acknowledgement of paternity document in order for SSA to process the minors application. It does NOT have to be DNA test verified.
SSA pays minors only till 18 or still in high school, unless they are documented disabled. All $ has to be spent too, it’s not to become a savings account.

Social Security will not tell you or your mother who is collecting benefits on your father's account. If the minor children were not listed in the obituary, unless you find a link through social media it may be impossible to find out. If your father was not listed on birth certificate documents as the father, you may never find out. If you know the county that the minor children were born in, you MIGHT be able to search birth records for the father or mother's name but it's hit-or-miss.

Google your father's name for an obituary. His minor children should certainly be listed there.