The glorification prayer you mean is salat-i tafrijiyyah. The narrations about it are true.

Salat-i Tafrijiyyah – Salat-i Nariyyah

“Allaahumma shalli shalaatan kaamilataw wasallim salaaman taamman 'alaa sayyidinaa Muhammadinilladzi tanhallu bihil 'uqadu watanfariju bihil kurabu watuqdhaa bihil hawaa-iju watunaalu bihir raghaa-ibu wahusnul khawaatimi wayustasqal ghamaamu biwajhihil kariimi wa'alaa aalihii washahbihii fii kulli lamhatiw wanafasim bi'adadi kulli ma'luumil lak”

Imam Qurdubi said:

“If one cites Salat-i Tafrijiyyah 4444 times in order for an important matter or a wish of his/hers to come true, or to get rid of an important trouble, and if he/she has the Supreme prophet as a cause for this wish with this prayer (dua), Allah will create good reasons for his/her will to come true and gives his/her wish.”

Translation: “Allah, may peace be upon our Prophet Mohammad and his family and companions in every blink of eye, in every breathing and as many as the things known to You. Upon Mohammad because of whom the knots are untied, because of whom troubles disappear, the needs are met, wills are reached and for his sake people pray for rain."