I have sole custody of my four kids and the father says he has rights to claim the kids on taxes. He only gets social security. Is this true?
The ability to claim children are typically addressed in divorce or separation agreements. Without the agreements in place, either the custodial parent or in some cases whoever files their taxes first typically is able to claim the dependents.
The IRS currently will mediate on who the correct person is to claim the dependents. If a person has the right to claim a dependent, but someone else does so and files their tax return first, then that person just needs to provide proof to the IRS that the are supposed to be claiming the child.
This happened to me, and I simply wrote a letter to the IRS included copies of the divorce agreement. The first year I received a letter from the IRS after I filed my return that someone claimed the dependents. I then responded with my documentation, which they accepted. In subsequent years, I just included the documentation when I filed my taxes.
From your brief description it sounds like the IRS would rule in your favor.