Should I request a recommendation letter?

I was working as an intern as a project Engineer for 8 months in this company. Then I managed to sign a for a position as Project Engineer for making good impressions when I was an intern, it only lasted for 3 months. I was interested in moving on to another area in the same company. Even I went to work Saturdays for free in that area I was interested on to acquire some experience. Then all this virus thing started to cause panic in the company and they began to lay off employees. Boss chose to lay me off because I was losing interest in the area and they were looking for people to develop a long term relation in that position.

Now Im worried that I might not be able to find a job right now and my resume will look weird having only signed for 3 months as Engineer. I know I was being efficient and making a pretty good progress there. Should I request a recommendation letter? and how should I approach?

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