Does a gap of 10 months after Master's degree affect my chances for a future academic career? I am soon to submit my PhD thesis and I am currently looking for postdoc positions. I would eventually like to stay in academia and was concerned if my past gap year would harm my chances in getting a position.

After my master's degree, I got an R&amp;D job and worked there for 4 months before quitting it as I did not enjoy it there. My plan was to join my master's lab as a research fellow, and I had an offer for that from my advisor. But, I got a bad disease and I fell ill for 3 months. I was not hospitalized, but had to live with my parents for the period.
As I always wanted to pursue PhD, I was searching for a position in the meantime. During the 3 months, I gave GRE (scored poorly, thanks to my illness) and applied to universities and professors. I got a positive response and I was sure of getting a PhD position.

However, it was already February and if I were to join a PhD program, I would have to wait till September. Also, the visa process and other formalities take time. So, I decided to not go further with the research fellow, and take time to complete the visa processing, spend time with parents and travel around.

I had a blast of time. Learned so much during that time. But, I don't have anything concrete to show for that 9-10 months period.

My concern is, how much will that affect my future career?
This will have essentially no impact on your career. Clearly it has no impact on your research productivity. So I don't see why anyone would take issue with it. Many professors have taken circuitous routes to get where they are, thus suggesting there are no expectations you complete all your degrees without any breaks in between.