I contracted out to have a privacy fence built. The contractor did not get a permit, and to top it off, the fence is out of plumb from 8 to 12 inches (leaning) in less than 3 months.

The city building inspector sent a letter stating I needed to come in and apply for a building permit. I did, and was charged a permit fee of $75.00 and a investigation fee of $100.00 dollars.

I tried to get the contractor back to correct his work that the city building inspector "failed", but am now having to take him to small claims court because he won't honor his work.

Now, the city building inspector (who I explained everything above to) has sent me a letter to pay an $80 permit extension fee.

First, am I not dealing with an "ordinance" with the building inspector, and do "ordinances" need a state law to give them authority?

Second, does the city have the authority/right to continue to charge me fees?

Yes, Larry, ordinances are law and enforceable by the sheriff if a judge enters an order directing the sheriff to take action. Sounds to me like you have a good small claims case against the "contract" who probably doesn't have a license, either, which in some states would result in a judgment far in excess of your actual costs, and since he breached his contract with you, you have an action to recover the cost of hiring someone else to come do it right ... with a permit. Hope this helps and that you are TELLING EVERYONE ABOUT MY COURSE!

Jurisdictionary,
How does an Ordinance become "law"?
Also, I thought I had read somewhere that an Ordinance HAD to have a State Law, or to cite a State Law to back it up, to make it valid with authority. Is that correct?

Each municipality has power to enact and ENFORCE ordinances, as I said above. If you wish to challenge same, my course is the very best tool you can obtain anywhere, however you will find the local law enforcement officers do have power, and it is power you really don't want to challenge unless you can prove you did not violate their ordinance in any way. To learn more about ordinances, please use Google and research the ordinances in your city or township to see that what I tell you is true. I want what's best for you, and fighting city hall (unless you are sure you've not violated any ordinance or other law) is not the best plan.

I agree that fighting municipalities is not the best plan. My reason: municipal officials are extremely corrupted. Municipal judges are ready to sweep a lot of dirt under the rug. This is coming from my personal painful experience.