بِالمَرْحَمَةِ

بِالمَرْحَمَةِ is a phrase (شِبْهُ الجُمْلَةِ) consisting of a particle of pulling down (a preposition) and a genitive noun

PhraseParticle / NounNoun Particle
شِبْهُ الجُمْلَةِجَارٌ وَمَجْرُوْرٌاسْمٌ مَجْرُوْرٌحَرْفُ جَرٍّ
PhraseCompoundGenitive NounParticle of pulling down/Preposition
  
to compassionبِالمَرْحَمَةِ=المَرْحَمَةِ+بِ
to mercymercythrough / to / in
Surah/Below is the only verse in the holy Quran containing the phraseبِالمَرْحَمَةِ
Verse
90-17then he became of those who believed and recommended to patience and  to mercyثُمَّ كَانَ مِنْ الَّذِيْنَ ءَامَنُوْا وَتَوَاصَوْا بِالصَّبْرِ وَتَوَاصَوْا بِالمَرْحَمَةِ