"especially written for" is correct and usable in written English.
You can use it when referring to something written specifically for a particular purpose, individual, or audience. For example, "This letter was especially written for the incoming class of 2021."
There is also a thought-provoking pack especially written for trainee teachers.
The story includes words and music to nine familiar carols and one especially written for the book.
This manuscript presents hydrogels (HGs) from a tissue engineering perspective being especially written for those who are approaching this field by offering a concise but inclusive review of hydrogel synthesis, properties, characterization methods, and applications.
Language lessons can be made topical with help from schools online news service The Day, which translates a selection of its daily news stories, especially written for young people, into the major European languages.
When he made Top Secret (1952), especially written for him, about a naive sanitary engineer with a revolutionary new idea which the Russians think is an improved atom bomb, even the film fan magazine Picturegoer questioned whether he could carry a film as its star.
Lyricism, the singing line, has always the vital spark in Hans Werner Henze's music, however much it has shifted its direction and changed its emphasis over half a century of composition, and his work list includes a number of scores especially written for great singers of successive generations.
Doogie had sang "Before The Devil Knows You're Dead," which is a song I especially wrote for him for the first Temple Of Rock album.
I doubt that learning to write a standardized test essay, especially one written for a computer, will encourage any student to explore the beauty of the written word.
Over his career, he has honed a signature sound that is spare and chiselled, especially when writing for voices.
Not because writing itself is difficult, although that fact is debateable, but because getting paid a living wage for your words is challenging in today's market, especially when writing for the web.
Despite what you've been told about the uncertainty that is inherent in science, many scientists are not above making unjustifiably sweeping claims, especially when writing for laypeople.
