I'm shocked that it's so hard to find the answer to this question:
How can I see which people following me also follow [some other person]?
Twitter uses this precise relationship to determine who gets to see a tweet I send to someone. The @user address form goes to the recipient and anyone who follows both of us.
How am I supposed to know who's following both of us? I can see a list of who is following me but I shouldn't have to go to every person's profile to see if they're also following person X.
Tell me twitter didn't implement a piece of recipient logic that fundamental and powerful, without allowing users to see the list of people their tweet is going to!
Best Answer
Short answer: It is not exposed in the web UI.
For completeness the first way you mention is:
https://twitter.com/USERNAME/followers_you_follow
e.g.
https://twitter.com/xsteenbrugge/followers_you_follow
Where you then have to look for "Follows you" badges in the displayed list.
The second way is using the intersection of API calls to this endpoint.
https://developer.twitter.com/en/docs/accounts-and-users/follow-search-get-users/api-reference/get-followers-ids.html
Where in the first call
user_idis your user id and in the second it's the other user's id.