How to fuse batteries connected in series?
The question contains some errors but I will try to answer what I think you are really asking.  You're talking about fuses (fuse wire) so clearly you are interested in trying to protect the circuit.

When batteries are connected in series, the same current flows through all batteries.  So you need a single fuse to protect them all.

Actually fuses are often used to protect the cable, and so fuses should be set to a lower rating than the current the cable can carry.

If you really are talking about resistors and putting them in series with the batteries: then standard formulae apply: power W = I.I.R  (I squared R).  V = I.R , W = V.I and all the other permutations of these formulae.

So you have to ensure that the power dissipated by the resistor does not exceed the maximum power rating for that resistor. If it does, the resistor will become excessively hot and burn out.

The voltage you know, the maximum current you know or you can calculate, and so you can calculate the power dissipated by the resistor.

You don't need fuse wire in each position. Fuse wire - of the correct rating - in one position is enough.

Let's spend a moment talking about fuse wire. Fuse wire is specified in Amps, as to how much current it can handle before it breaks.  Fuse wire is not specified in W - watts.

Watts = volts x current. And the voltage doesn't matter, because it's an electrical conductor (made of metal), the voltage at any point along the fuse wire is the same (that's not entirely true, but good enough for discussion here).

So you're only interested in current when talking about fuse wire, which is measured in amps.