Can neighbor build a fence to enclose a stripe of my land?

What is the name of your state?Georgia.

We live in a relatively new subdivision. We build our backyard fence when our left side neighbor's house had not been build. To avoid any possible disputes and following the guidelines of HOA, we build the fence completely on our proporty --actually one foot from the property line. Now, our neighbor is building their own fence. However, instead of building a complete fence, they just used my left fence as their right fence and built a segment to connect my fence to their house. This bascially converts my fence into a mutual fence and encloses my one foot land stripe into their yard. The neighbor does recognize our claim that our fence is not the property line. But they insist that it is a common sense for them to just connect my fence to their house. What is my legal base to ask them to build their own fence? And can I ask them certain compensation for sharing my fence?

You can tell them to take their fence off of your property, you can ask for compensation for 'leasing' your land to them or you can file a complaint with your HOA.