Index on a partitioned key we have a list partitioned table. Let partitioned column be c1. We have an index on that column(c1). We are planning to drop the index. Our doubt is that if we drop the index, does it affect the performance? Suppose we are querying one of the partition. Does the oracle optimizer directly use the partition segment or rely on index(on the partitioned column) to choose the correct partition or does it perform a full table scan (going through all the segments) if we delete the index?
First, you can try to monitor index usage.
You will take the answer used index or not used.
Index monitoring can be switched on/off several times to get more information.

For example, here: https://oracle-base.com/articles/9i/performance-enhancements-9i#IndexMonitoring

Also, you can look into v$sql_plan view to see what recent queries used this index:

select s.sql_id, s.sql_text
  from v$sql_plan p, v$sql s
 where p.sql_id = s.sql_id
 and object_name = 'YOUR_INDEX_NAME_HERE' ;


Also, and most importantly, you can make the index invisible for the optimizer.
That way you can clearly see if it affects performance of your queries.

Examples - https://oracle-base.com/articles/11g/invisible-indexes-11gr1