Routes in ASP.net Core API

Try this. You can put a common route prefix on the controller.

[Route("api/[controller]")]
public class BXLogsController : Controller {
    //GET api/BXlogs/id/blah
    [HttpGet("ID/{id}", Name = "GetL")]
    public IActionResult GetById(string id) { ... }

    //GET api/BXlogs/api/blahapi
    [HttpGet("API/{apiname}", Name = "GetLAPI")]
    public IActionResult GetByAPI(string apiname) { ... }
}

read up on attribute routing here Routing to Controller Actions

In case if you're planning to have a custom action name similar to web API's.

 [Route("api/[controller]")]
    public class BXLogsController : Controller {
        //GET api/BXlogs/blahapi
        [HttpGet("{apiname}", Name = "GetLAPI")]
        public IActionResult GetByAPI(string apiname) { ... }
    }

a little extended to @nkosi

So you'll be calling as

GET: https://localhost:44302/api/BXLogs/GetLAPI