Lookup only for odd or even numbers into the list

I'm trying to understand how to search separately only for odd or even indexes with random int rndIndx = random.Next(0, 6); value into the List<string> List = new List<string>(); For example content of list:

string 0 even
string 1 odd
string 2 even
string 3 odd
string 4 even
string 5 odd

I'm not sure how to avoid accepting of one or another to not skip process if random value is odd when I have search for random into even indexes

Another way, if I can somehow search only for odd or separately for even indexes for list itself.

If I can find string by index, then I can use conditions rndIndx % 2 == 0 but anyway I can skip needed process if result is not acceptable for condition

The best way to get desired result would be if I can somehow avoid search for excepted numbers of indexes into the list, additionally it could optimize the performance because in case of Odd I don't have any reason to look for Even number into 90000 values, even if I can except it, and vice versa. But I'm not sure how to do it.

Or I need to repeat request for random number with while loop until the value does not match to the searching type number, not sure if it is better way