You should be able to run a SQL statement using the PostGIS function [ST_LineLocatePoint][1] to select the relative distance along the route.  You will need a single route, a filter for the max distance from the route, and an order by clause.

This is untested, but should get you started:

    Select    points.pointID
    from      points, 
              rountes 
    where     rountes.routeID = :routeid 
      and     ST_Intersects(points.pointShape, ST_Buffer(route.rounteShape, 50000))
    order by  ST_LineLocatePoint(route.rounteShape, points.pointShape); 

You could filter by ST_Distance(points.pointShape, route.routeShape) <= 50000, but I'm not sure if that is going to use the spatial index.

  [1]: https://postgis.net/docs/ST_LineLocatePoint.html

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