I have a trucking business where I hire myself out to other carriers. Want to
Know if the gas I use to perform this service for other carriers would be charged to
Fuel Expense or does it go to COGS?

Normally service companies will not have a COGS account. COGS stands for Cost Of Goods Sold. You are providing a sercvice, not selling goods. COGS is used by a manufacturing company because they make and sell goods.

As a service company you should use an expense account like Fuel Expense.