hi,

see you are eligible to apply for gate exam from any stream if you have fulfilled the eligibility criteria, however there is no syllabus for mechatronics engineering since there is no paper for mechatronics engineering. you may appear from mechanical engineering if you find the syllabus topics is in grip of yours. follow below link to know about mechanical engineering gate syllabus,

https://engineering.careers360.com/articles/gate-syllabus-for-mechanical-engineering