The protection fuse, if that is what you have, goes on the bottom or negative end of the battery when in the mod. It should attach via small magnet.
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There two types. A single use one, and one that can be used multiple times.
Yes, you should use a mod fuse. All battery driven devices need some sort of protection. Mechanical mods have no protection built into the mod, unlike regulated VV/VW mods whose processor provides protection against short circuits in the heating coil and the battery.
Tell us what battery you are using? Name brand and numbers/letters on the battery? Depending on where you purchased your kit, it may be the wrong battery for your particular mod. Just because they send you batteries with the mod that's not to mean its the correct type. There are IMR, protected lion, unprotected lion, and hybrid types.
Some useful resources for you to learn:
Mechanical Mod Proper Usage Guide
Vape Safe Mod Fuse
Battery Basics for Mods: IMR or Protected?