Please help identify this for us

[Allen Reed]

I would appreciate as much information as I can get on this shotgun please. It’s been in the family for a few generations now. I’m sure you get posts like this often so I apologize about my lack of knowledge. Thought you all would have the knowledge and expertise. It’s a 12 gauge with a 30 inch barrel. Frame size says 02. Says Parker Bros Makers Meriden Conn Twist on the rib. Serial number is 35801. I removed the barrels and stamped on the receiver is the letter T with a circle around it. Then to the top right of it is a letter J. Any information for my family would be awesome! Any thoughts on what these sold for back in the day? Thank you for your time!! I’m an avid hunter but I know little about older guns like this.
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