I Am Legal Heir To Deceased's Estate In Texas, But I Am Not A Texas Resident Nor Can I Appear In Texas. What Can I Do?

My dad passed away several years ago, and I recently discovered he had multiple bank accounts that are essentially just sitting with unclaimed money. I'm trying to research how I can get this money transferred to me as the legal heir. Everything seems to be pointing towards filing a Small Estate Affidavit with the probate court, but it also seems it must be done in person with a clerk; I cannot find efiling options. I am unable to go in person for this, as I am living in Connecticut.

Additional context and info that may help?

• My dad was born in CT, moved to TX later and was a legal resident of TX for the rest of his life. He lived in Denton County.
• I myself have never lived in or been a legal resident of TX.
• I am the sole heir to my dad's estate. He had no spouse and I was his only child.
• He left no will.
• The total amount of money is under $45k (I believe that is the amount limit for small estate affidavits).
  

I hope to find some guidance. Inheriting this money would help me immensely in the current financial bind I am in, and of course my dad would have wanted me to have it, not have it sit forever owned by the state.