Thanks genomax. I scanned the reads and got adapters. My sequencing facility did not remove adapters.Since my main goal is calling variants from the reads, the adapter bases will anyway have lower base qualities and while mapping to the genome also may be soft clipped (using BWA mem here). Furthermore, GATK (variant caller of my choice) in itself handles bad base and mapping qualities by itself (through its default paramters, not getting into details here).
It has also been mentioned in their website (various places) not to trim the reads at all. I personally haven't done any benchmark at my end, but theres a trend of not trimming reads at all. How far is this advisable in my case here?
The overrepresentation in FastQC is computed on the reads' first 50 bp. Your adapter sequences are popping up further downstream.