I don't think that sample size influences whether or not publication bias will occur. The bias could arise from the findings of the researchers and whether they want to publish their work. On the hand, the journal may not publish the article for one reason or another, irrespective of the sample sizes in the study.

Hi Adedoyin, 

For a sample size, there is not a specific number, in SR or MA, to avoid publication bias. I think you are referring to "inclusion criteria" when you mention barriers for studies included in

I think you are referring to "inclusion criteria" when you mentioned barriers for studies included in your SR or MA. You must create your own inclusion criteria that will allow you to select the papers you are looking for to answer your research question. 

Hope this helps and happy to continue the discussion. 

Do  a Funnel plot to find out Publication bias. But there can be various other forms of bias in SR and MA one needs to take care of. Concerns may be for Grey literature. So extensive search of article for relevant sources is required.

There is no sample size important here. As you will be selecting already published data done on various samples. The methodology followed in each study and what is results of your interest were interpreted is important for you to see.. Start with the PICO strategy and as others have suggested above, you have to be specific about your research question and have proper inclusion and exclusion criteria framed.