Drag a object along curves

Hi I want to drag an 2d object along a curvy 2dpath
if the player drag in right path the object gets drag or else not , check the file attached

what I tried is on mouse drag I raycast through the object and checked if it hit the path then move else not but its not working smoothly and the object freezes

 RaycastHit2D hits;![alt text][1]
     hits = Physics2D.Raycast(transform.position, -Vector3.back, 10000f,7) ;
     if(hits.collider != null && hits.collider.tag== "path" )
     {
         Lastpos = hits.point;
         Debug.DrawRay(transform.position,-Vector3.back,Color.green,Time.deltaTime*10);
         print (hits.collider);
         Vector3 pos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
         transform.position= new Vector3(pos.x,pos.y,-0.1419618f);

     }

 

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[1]: /storage/temp/42981-pathline.png