If you are using advanced search web part and want to add your own custom property to the properties list, then you can do it very easily.
First you need to have managed property which is mapped with the crawled property. If you would like to know how to get crawled property and how to map the managed property with the crawled property, you can refer
Consider we have one advance search web part and a managed property with us. Go ahead and edit the advance search web part.
Prior adding our department property that we already have , let us see what all things that we can do with advance search web part.
If you remove all which is highlighted in above image, you can see that languages options go away from search.
We also have the document type
If you remove all which is highlighted in below image, you can see that excel and powerpoint document type option go away.
and here is what you get.
Now you should be able to get the results by specifying your custom property. I hope this helps.