Eventually FortranTip will cover OOP in Fortran. I will first suggest free resources such as the following. Further suggestions are welcome. There are also Fortran 2003+ textbooks.
Object-Oriented Features in Fortran 2003 by Reinhold Bader
Object-Oriented Programming in Fortran 2003, by Mark Leair. Parts 2 3 and 4. Also here with some discussion.
Scientific Programming in Fortran 2003: A tutorial Including Object-Oriented Programming by Katherine Holcomb (chapter 11)
Introduction to Advanced Fortran from PRACE (pp22-39 of pdf)
Modern Fortran in Science and Technology by Jonas Lindemann and Ola Dahlblom
Not My TYPE by Steve Lionel discusses type extension and polymorphism
The following compiler manuals have sections on OOP:
Edited 2022-03-29 to add:
At FortranCon 2020 @Arjen conducted a workshop on OOP, with videos here, slides here and here. Codes from his book “Modern Fortran in Practice” are here – chapter 11 is on OOP.
At the same conference, Tiziano MĂĽller gave a presentation OOP Fortran: About constructors and practical applications of patterns, video here.