Over time, I have seen a LOT of carbs with either aluminum or zinc air horns where the fuel inlet fitting bottoms out. This is caused by "its tight", "well give it another 1/4 turn". Each time the fitting is tightened beyond the necessary torque, a bit of thread in the casting will be removed, allowing the fitting to screw further into the air horn.
The use of teflon tape can also cause this issue, if the tape uncovers the brass thread, the overall diameter of the fitting and thread will cause the bare thread to cut into the housing.
There at least two "fixes".
(1) If the carburetor in question is from a supercharged Duesenberg or a V-12 Packard, or, or, or, where the value of the carburetor exceeds the value of a totally restored 3100 Chevy, you fix the issue. This is best done by machining a new fuel inlet fitting on your lathe with the male thread a few thousandths oversize. The oversize thread will prevent the fitting from bottoming and allow it to seal; until "give it another 1/4 turn" a few times.
I do not know if tooling is currently available to cut the female inverted flare portion or not. 40 years ago when we were restoring factory multiple carb setups, and special fittings were not expensive, simply because they were not available to be expensive. I paid a tool and die maker a pretty good chunk of cash to machine special tools to allow me to do the female inverted flares. If I can do it, so can others; it just costs money!
(2) If the carburetor in question is not appreciably valuable, pitch it, and start with another carburetor.
I would concur with others about determining the source of the leak. I like Jon G's comment about the old T-shirt. My approach is to dry the area as much as possible with paper towels, they use a blow hair dryer (not mine, I don't need one for half a dozen hairs

) to thoroughly dry the area. Once dry, one should be able to start the engine, then watch it run at an idle until the leak appears. Once the source of the leak is known, it is much easier to determine a fix or replace.
The other Jon