I'm not licensed in your state but usually if you are filing some sort of Answer to a lawsuit, your Mom has to answer it but anyone can take it to the Clerk's office and pay the fee, if any, to have it filed.
I'm not sure what you mean by "sworn denial." If your mother is being sued for a debt, chances are, she needs to sit down with a lawyer and talk to him or her about it. Parents tend not to talk to children about their debt. It's possible that she DOES owe the debt, it is also possible that if she owes the debt, she may have defenses that she may need to affirmatively assert otherwise they will be waived.
It is also possible that she doesn't owe the debt - and one of the reasons may be that her identity has somehow been compromised. She should check her credit report and see what's there.
If the courts are involved, have your mother speak to an attorney and treat this legal matter with the seriousness it deserves.
If your mother is being sued on a debt, you should hire an attorney to prepare and file an answer and any other appropriate paperwork. Unless this is small claims court, I would not recommend defending a lawsuit against a debt collect without the assistance of an attorney.