"specifically asked that" is correct and commonly used in written English.
It is typically used when someone has made a specific request or question. Example: During the meeting, I specifically asked that all team members submit their reports by Friday.
Governor Bentley specifically asked that legislators reconsider one section in the new bill and another in the original one: the new provision that compels the state to list the names of illegal immigrants who appear in court; and the section of the original law, currently barred by a federal court, that requires schools to ascertain immigration status.
He specifically asked that his death not be used for political purposes.
Ms. Watkins, you specifically asked that Vinson & Elkins not do this investigation.
At his October 2004 review hearing, Mr. Hekmati specifically asked that Hajji Zaher and Mr. Khan be contacted to act as supporting witnesses.
He specifically asked that, following the appeal process of the two youth activists, the President find a way on humanitarian grounds to release the two men.
"You can ask pretty much anything," the PR woman told me before our interview, "but he's specifically asked that you don't talk to him about his hobbies".
Find a mentor and specifically ask that person to be your mentor.
Similarly, the Andante movement of the A minor Sonata, sad though its message, specifically asks that its tempo walk as it did here, not trudge.
Often when the president dines out, the event is more public, in that his staff might specifically ask that other diners sit at tables directly around Obama.
The epiclesis specifically asks that bread and wine be made the body and blood of Christ, and the actual change (Greek: metabolē) is attributed to the Holy Spirit.
The presentation of appraisal results must be balanced, highlighting the areas where ratings or viewpoints diverge and preserving the anonymity of individual members unless individuals specifically ask that their names be used.
