Note: The requested logs contain all the log rotations for that log type that exist on the BIG-IP system. For example, BIG-IP LTM logs are combined from /var/log/ltm, /var/log/ltm.1, and /var/log/ltm[2-9].gz, if those log rotations exist on the system. Additionally, when specifying options=lines,10, this means the first 10 lines of the oldest logs found for that log type. You can refer following kb article for more options:
K41550738: Viewing BIG-IP log files using the iControl REST API
Thanks for the details, I have tried this way and I was able to get the data from specific time stamp.
Also I wanted to get the data which is greater than the time, but now I am getting the data which is greater than or equal to the timestamp. Is there any way to get data which is only greater than the specfic time.