C# Overload method with var type

I am querying a SQL database via LINQ in my C# project and returning the data to a var type variable

The type of the variable isn't var - that's just the form of declaration you're using. The type of the variable is whatever the compiler infers it to be.

How can I overload a method with var type?

You can't. var isn't a type.

Unfortunately, we don't know what you're trying to do in method. Maybe you want to make it a generic method. Maybe you want to make it take object. If you're actually trying to use an anonymous type, and pass values between methods, then you're probably best off creating a named type with the relevant properties.