Is it advisable/sufficient to enroll and finish my MSc degree in an accredited private university in the same country with no ranking in Times or QS? I have dropped out of 2 MSc in CSE programs because of my health issues and lack of proper math background.
You can check the full story from my previous question.

What should I do now to go ahead and restart my aspirations to become an appropriate candidate for a Ph.D. program?

Some answerers suggested that I should go back to my incomplete M.Sc. degree. Another answerer in the comment suggested that even though my dropped master’s degrees were 2y in length, completing 1y or 1.5y programs will also be sufficient.
My new question is, does the reputation matter in this case if the program is accredited?
My previous universities were state-run mainstream universities with the times Subject-rank of 601-800.
Is it advisable/sufficient to enroll and finish my MSc degree in an accredited private university in the same country with no ranking in Times or QS?
In the short term, what you are asking is that the &quot;new&quot; university accepts some of the exams/courses/credits you gained previously.
That's entirely up to each single university how they will manage that. You need to get in touch with the universities you are aiming at.
Your goal is to complete a MSc, they usually are 2 years in length (read: they require you to pay 2 years of tuition fees) but how you complete this journey (if you pass the exams or if you can have the past exams recognized) it is entirely to the single University internal regulations.
However, in the long term the lack of proper math background is what should worry you, more than the rating/ranking of a specific university, especially if you aim at pursuing a PhD.
Good luck, from what I understand you feel a bit of time pressure. Don't. Many PhDs in Europe start their PhDs when they are well over 25 years old, even around 30 years old, so do not rush and take your time.
Especially in having good math fundamentals, if your goal is to pursue a PhD.