In some articles I have seen that for screening of a specific gene the authors just used a primer set and then sequenced the fragment. But, in other articles, after PCR, fragments were cloned and then sequenced. What is the difference here?
Your question is still not clear. Are you intending to look for the expression levels of a specific gene, mutations, ...? Just doing a PCR won't tell you anything about the special function of a specific gene. If you are seeking advice you have to provide some more details or simply ask you supervisor.