Q: Are there any other documentation I can present to prove my case in acquiring a US Passport?

A: You state that they shared custody. Actual physical evidence of this shared custody. Evidence that may meet the requirement is based on personal circumstances. The request provides you with examples of documentation for meeting this requirement. You may want to work with an experienced immigration attorney.

A: " Evidence that shows I was in the sole or joint legal and physical custody of my US citizen parent pursuant to lawful admission for permanent residence such as a custody decree or the death certificate of my non-US citizen parent. "

You may consider sworn legal notarized Affidavits prepared by an experienced immigration attorney to prove up the above.

"A combination of documents such as school, tax, medical or court records that documents I was in the legal and physical custody of my US citizen parent after I entered the US for lawful permanent residence and before my 18th birthday. "

Your father's tax returns listing you as a defendant would be helpful, your school, court records, insurance plans that show that your father asserted physical custody over you.

"My father was never married to my mother. They both shared custody. My father's name is on my foreign birth certificate. My mother is alive. I did not acquire any of the documents requested before my 18th birthday as I was only in the US for 19 days before my birthday. I have supplied LPR card and SSN to them."

The submitted documents are insufficient to prove up your case.

You need to consult further with an immigration counsel of your choice directly.