Can I fix a leak at the fitting for my hot tub without turning off the water? Is there a putty or tape available

Plastic? Metal? Tapered threads? Compression fitting?

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Are we talking about something unusual because the hot tubs I have set are not plumbed. Where is this supply line going or did you mean a whirlpool?

Sagginsuzie... there are repair tapes available at your local home supply store if you are looking for a quick fix so you do not have to drain the hot tub... but if a whirlpool (as Ballengerb1 questioned.. )... you will need to find a more permanent solution to your problem.

Anyway, answer the questions posed by posters and we will see what else we can do.