Under edit on messages my drop-down menu does not include “ recently deleted messages“ how can I retrieve deleted messages?

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You may get better and prompt responses if you may kindly provide the iPhone Model that you have and the iOS version if it is known to you and re-post.

With the limited information that you have provided, It is hard to even guess the problems faced by you. 

You may get faster and better responses to your query by --> Writing an effective Apple Support Commun… - Apple ...

Please re-post with detail so that someone else can help.

Probably you are not on iOS 16 or above.