Will a High Output alternator use more gas because it's harder to spin?

I have a 2001 Ford Crown Victoria with the P71 police package.

The car is supposed to come with a 220 amp alternator. It was removed and there's a 135 in there now.

It is dying. If I get the 220 amp alternator, does it use more gas? If so, how much?

It does require a stronger pulley for the motor, and weighs two pounds more.

Some people say it has heavier windings to turn? Is this true?

Basically, what I need to know is whether a HO alternator (that is actually specified for my vehicle) would result in a loss (even a little) of gas mileage.

Of course it does. There's no free lunch. It takes more power to make more power.

The load is dependant on requirements. So a low output alternator may have to run much longer to fully recharge a battery than higher output. Also load isn't an on -off things but can be fully loaded or partly again depending on alternator excitement needed to give output required.
in short it will add weight to car and technically increase fuel usage but running costs will be same or lower than one you have now.
this is why the original was designated by manufacturer. They never add more cost. Weight than needed.
we will use more just using ac on for each journey. For fuel saving.ensure car is kept in use with clean air filter serviced regularly. No excess weight in car or roof racks. No speeding. Gentle driving and low ruling resistance tyres.

More resistance more fuel you get what you pay for

A larger alternator will not take an appreciable amount of effort to turn by dint of its size.

However, an alternator under load is harder to turn because the magnetic field exerts a force on the armature. So, the more power you use, the harder it is to turn. A larger alternator can supply more power, so potentially it could make a greater drag on the engine if you were using that extra power.