Courses outside colleges and do they count?
NPTEL is the best bet.
It is a MOOC by the Government of India, where online courses are offered by various Indian universities, including the IITs and the Indian Institute of Science. It is similar to Coursera and such in the sense that you watch videos and complete weekly assignments. You can register yourself as a student through this link and browse courses.
If you want your learning to be certified, you need to register for a particular course. Registration for courses happens twice a year (just like usual colleges). Unfortunately, I believe you have missed the registration deadlines for most of the Jan - April courses, there are only a few that are still available.
For example, this is the catalogue for the courses you can still enroll for during the Jan-April 2021 phase in Mathematics. Perhaps a course may interest you.
You can also wait for registration to open again for the July-November set of courses (this starts sometime in June-July).
How it works

You can browse for various courses using the Course Catalog tab.

Register for the courses you are interested in. Duration of the courses are typically 8-12 weeks.

Go through the uploaded video/text lectures (this depends on the course).

Complete the weekly quizzes and other assignments as applicable to the course.

Register for the final exam within the mentioned deadline. Without writing the final exam, you will not be provided the certificate.


The Final Exam

The final exam is usually written at designated test centres in March or April for the Jan-April courses, and in September or November for the July-November courses. Choose your test centre carefully.

All the final exams are conducted on Sundays, either in the morning slot (9-12 PM) or the afternoon slot (2-5 PM). If you are attempting the final exam of multiple courses, make sure they do not clash.


Note: You can attempt the final exams for a maximum of six courses per 'semester'. Also, there is an exam registration fee of ₹1,000 per exam.
Getting certified
There is a specific set of criteria that needs to be met for you to be certified. This may vary from course to course, and it is mentioned clearly in the course information. For example, these are the criteria for a course called &quot;Introduction to Astrophysical Fluids&quot;.

Average assignment score = 25% of average of best 8 assignments out of
the total 12 assignments given in the course. Exam score = 75% of the
proctored certification exam score out of 100
Final score = Average assignment score + Exam score
YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT
SCORE &gt;=10/25 AND EXAM SCORE &gt;= 30/75. If one of the 2 criteria is not
met, you will not get the certificate even if the Final score &gt;=
40/100.

Most courses seem to have similar eligibility criteria.
Transferring Credits
There is an option in NPTEL when you register for the courses to transfer the credits to your university. But you need to talk to the academic department of your university about this beforehand. I would suggest you talk to your university at the beginning of the semester in which you are planning to take the NPTEL course. You need to know if:

They even consider an NPTEL course to be eligible to be added to the official transcript (and if they do, the procedure for it).

Whether they will consider it a 'pass/fail' course where you only need to submit your final certificate to show you have taken the course and it will be marked as a 'Pass' or whether your grades in the course will also be shown in the transcript.


For example, in my university, NPTEL courses are considered purely for extra credits as 'pass/fail' courses, meaning the grade I have achieved in the course will not be shown in my official transcript.
The Value
I cannot comment with certainty about this since I am an undergrad student like you. My assumption is this (needless to say, take it with a grain of salt):

Under normal circumstances, an NPTEL will probably carry lesser 'value' than a typical university course since the assignments are online and there are no 'classes' to attend. But remember that since we are writing a proctored final exam in person (much like a university course), it probably carries more weightage than certified courses of foreign MOOCs like Coursera or Udemy.

Under the current COVID situation, I would say an NPTEL course is very similar to the online university courses (In fact, many of my professors ask us to refer to archived NPTEL courses i.e. courses that are not accepting enrollment anymore, for the material). We complete weekly online assignments and write a proctored in-person online exam, similar to a university course. I would say that in such a situation, an NPTEL course should be considered to have the same value as a normal university one.

Furthermore, if your university only accepts the NPTEL course as a 'pass/fail' course, there is no indication of your performance in the course, but only evidence that you have taken it. In such a situation, the course would not carry as much value as a typical university course.


Final personal thoughts
Overall, I would suggest you take an NPTEL course (or two). The best-case scenario would be that you do well in the course and it reflects in your official transcript. If not, you still have a certificate that you can add to your CV or mention in an interview.
With regard to transferring credits through an online course, NPTEL is surely the best bet for Indian universities. I highly doubt they take certified courses from Coursera/Udemy/EdX seriously enough for credits transfer.