Normal Correlation is for paired observations, however you may use the same method by taking maximum paired observations for both the variables.

Also the following link may help you:

https://www.researchgate.net/post/How_to_do_correlation_analysis_with_two_variables_in_different_sample_size

Please check it up:

https://libguides.library.kent.edu/SPSS/PearsonCorr

Good Luck.

Following answers

In my opinion, before you begin to choose the appropriate statistical procedure you should look at the data in a close look at multiple ways before you engage yourself in complex statistical procedures, and to take an example to clarify this point you should write your notes carefully after looking closely at the data under your hands, rearrange them and match them in terms of number and type until you see for yourself how to access information about them before being subjected to statistical analysis may make sure that some information does not have any connection to the problem of search and be abnormal, which requires deletion.

I go along the recommendations given by Omran. Further I recommend that form your data pairs of the variables (miRNA, lymphocyte counts) very carefully. Check the relationship between the variables visually may be using a scatter diagram. Based on the visual check you get some idea weather a linear or non linear relation exists. Then decide what type of correlation will best describe the relation between your data pairs.