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I have a sample of people, around 1140 participants but not all of them answered all questions. I have to do correlation with variables , each with different sample sizes. I have 3 variables and they have a small difference in sample size: V1 (1135), V2 (1132) and V3 (1137). Can I do correlations with such variables? If not, what is the procedure?

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Have you tried resampling?

You can't calculate correlation coefficient for data that is not represented in pairs, so you could, for example, try this:

1. Take a random subsample of 1132 from $V_1$ and $V_3$ variables when correlating it with $V_2$, so that $V_2$ and $V_1$ or $V_2$ and $V_3$ have the same sample size. Note that samples are taken with replacement.

2. Calculate the correlation coefficient between the two samples.

3. Repeat the procedure many times (I'd suggest at least 1000 times)

After that, you can calculate the average value of correlation coefficient, as well as its confidence interval. This is also known as bootstrapping technique.

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