hi,

see in gate 2022 latest website information, there is no gate paper on mechatronics engineering. you  may take any of the paper available to appear in gate 2022 irrespective of your undergraduate b.tech stream.

now coming to the use of gate score, gate score is mostly accepted  for admission to m.tech course, psu hiring. however mechatronics engineering is quite new stream and according to past few years data available on psu hiring less or none vacancy for mechatronics engineer.

however by appearing in gate exam from the mechanical or cse or ece stream as per your choice you may be able to do m.tech and then get  job in campus placement in relevant discipline.