I want to create a REST service which returns results of my SPARQL queries as JSON. I worked with Apache Fuseki (on a local host) and there were some options to return the results as JSON. I want to run something like this on my server rather than my local host. Is it possible to have something like this (i.e., which returns results as JSON) on my server?
There is no qualitative difference between running something on your localhost and on a remote server. The program running on localhost to answer your calls locally /is/ a server. The exact same deployment on a computer acting as an internet visible server would do what you describe in your question.