Part Time

For admission into MCA, the candidate must be graduate with Mathematics or Statistics as one of the primary subjects at the degree level and Mathematics at the +2 level. In addition, the candidate must also qualify the DEET.
Meanwhile, any graduate who studied mathematics or statistics as one of the primary subjects at degree level, and mathematics at +2 level, can apply for admission into the M.Sc program. They wont require appearing in DEET or any other entrance test.
Only those who can furnish all necessary documents, including either Provisional or Degree
Certificate, as well as the marksheets of all the semesters at the time of the admission, will be eligible to apply. Those who obtain their undergraduate degree via the Off Campus route are not eligible.
Also, those who have already enrolled themselves for another program or are still undergoing the program, will be rejected.

As far as I know, there is no part time IIT JAM. You will have to devote yourself to the exam if you want to secure a passing grade in the exam and qualify for M.Tech or M.Sc.
JAM 2018 eligibility criteria:
The common criteria across institutes for each programme are:
JAM eligibility criteria is common for each program across institutes for appearing in the postgraduate science admission test.
The candidates should have secured at least 55% in subjects including languages and subsidiaries of all the years combined. Those, however, belonging to SC/ST and OBC categories need to secure at least 50 percent marks in the subjects.
Candidates need to note that equivalence of marks in case of grades in letter/CGPA (and not in percentage of marks) will be decided by the participating institutes of JAM.
As per the JAM eligibility criteria 2018, candidates will need to submit their proof of qualifying degree examinations by September 30th, 2018 to the admitting institute. However, upon failing to do so will lead to cancellation of their candidature.