the partition drop from parent is taking longer as it scans all the partitions of the child table
Does the relevant supporting index exist on the child table?
Yes all the child tables have foreign keys indexed.
Again I don't want to divert the main topic(trigger creation) . I will provide the exact test case how it puts exclusive lock and runs longer as scans all child partitions (which must be using indexes though) but as the number of partitions increase the time of drop partitions increases.