Try to find him a home first. Some cats like being outside. I feed several cats where i live. I also put an out door cat house/ small dog house with a thermal self heating pad for them to go in when it's cold. If you have to bring him in, call ahead. I had to do that with a 6 week old kitten.
I did not tjink there was a fee to bring strays.
You can drop animals off for a fee but it's recommended if you can to try and rehome him personally to someone you know as the shelter life isn't easy for animals once entered
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