If you did not sign the lease or otherwise agree to be responsible for your father’s obligations, you are not personally liable for any damages related to his apartment. Children or beneficiaries of a decedent’s estate (your father's estate) are generally not responsible for the debts of the deceased unless they have explicitly agreed to assume those debts.
However, if your father had an estate—meaning assets or property left behind after his death—the personal representative (executor) of that estate has a duty to settle his financial obligations, including paying any legitimate claims for damages made by the landlord. The landlord can file a claim against the estate to recover costs for damages. This process is handled through probate court, and the landlord would need to follow the proper procedures to make a claim against the estate, not against you personally.
If you have been contacted regarding these claims and there is no estate or personal representative, you may need to inform the landlord of this and decline responsibility. A consultation with an attorney would be helpful. If you would like our help, please feel free to contact us at (303) 688-0944.