Hi Shenaynay,
 
With many public schools, there are particular residential zones that one must reside within to have your child attend the school, or else you have to request permission to transfer in. However, according to this high school's page in SchoolFinder, Thomas Proctor High School is a magnet school that is open to students outside the normal school district boundaries.
 
I recommend you contact the school directly to learn more about its enrollment policies:  
 
Thomas Proctor High School
http://www.education.com/schoolfinder/us/new-york/utica/thomas-r-proctor-high-school/
 
I'm also including below some additional resources you may find helpful for your family. Good luck!