Masjid-e-Zu-Qiblatain (Mosque of Two Qiblas).The mosque where the Holy Prophet [s] was commanded to change his qibla from Masjid al-Aqsa (Jerusalem) to the Holy Ka'aba (Makkah)
In the sixth month of 1st Hijri, the Prophet (s.a.w.a.) visited the tribe of Bani Saalim which is in the north-west of Medina on invitation by Umme Bashar. As usual, he prayed two units of Zohr prayer facing Bayt-ul-Muqaddas when Allah ordered him to face Kaba. He continued the remaining prayer facing Kaba. After that, Kaba became Qiblah of Muslims forever. Hence this mosque is called 'Masjid-e-D'uqiblatan' or 'Masjid-e-Qiblatain' (The Mosque of Two Qiblas). This mosque is a little away from Mosque of Fatah towards the west.
This is a verse among the verses revealed on this incident.

قَدْ نَرٰی تَقَلُّبَ وَجْهِكَ فِی السَّمَآئِ فَلَنُوَلِّیَنَّكَ قِبْلَۃً تَرْضٰیهَا فَوَلِّ وَجْهَكَ شَطْرَ الْمَسْجِدِ الْحَرَامِ وَ حَیْثُ مَا كُنْتُمْ فَوَلُّوْا وُجُوْهَكُمْ شَطْرَهٗ…۔

"Earlier there were two arches (Mehrab) opposite to each other - one facing Kaaba and another Bayt-ul-Muqaddas. Unfortunately, only one arch remained when the renovation of this mosque was done a few years ago. The first signs of this incident were erased."
It is mustahab (recommended) to pray 2 rakats Namaz of respect in this Mosque. It is better to recite the following Dua after the prayers:

اَللّٰہُمَّ اِنَّ ہٰذَا مَسْجِدُ الْقِبْلَتَیْنِ وَ مُصَلّٰی نَبِیِّنَا وَ حَبِیْبِنَا وَ سَیِّدِنَا مُحَمَّدٍ صَلَّی اللّٰہُ عَلَیْہِ وَ آلِہٖ وَ سَلَّمَ اَللّٰہُمَّ اِنَّكَ قُلْتَ وَ قَوْلُكَ الْحَقُّ فِیْ كِتَابِكَ الْمُنْزَلِ عَلٰی صَدْرِ نَبِیِّكَ الْمُرْسَلِ: قَدْ نَرٰی تَقَلُّبَ وَجْهِكَ فِی السَّمَآئِ فَلَنُوَلِّیَنَّكَ قِبْلَۃً تَرْضٰیهَا فَوَلِّ وَجْهَكَ شَطْرَ الْمَسْجِدِ الْحَرَامِ‘ اَللّٰهُمَّ كَمَا بَلَّغْتَنَا فِی الدُّنْیَا زِیَارَتَهٗ وَ مَآثِرَهُ الشَّرِیْفَۃَ فَلَا تُحْرِمْنَا یَا اَللّٰهُ فِی الْآخِرَۃِ مِنْ فَضْلِ شَفَاعَۃِ مُحَمَّدٍ صَلَّی اللّٰهُ عَلَیْهِ وَ آلِهٖ وَ سَلَّمَ وَ احْشُرْنَا فِی زُمْرَتِهٖ وَ تَحْتَ لِوَآئِهٖ وَ اَمِتْنَا عَلٰی مَحَبَّتِهٖ وَ سُنَّتِهٖ وَ اسْقِنَا مِنْ حَوْضِهِ الْمَوْرِدِ بِیَدِهِ الشَّرِیْفَۃِ شُرْبَۃً هَنِیْئَۃً مَرِیْئَۃً لَا نَظْمَأُ بَعْدَهَا اَبَدًا اِنَّكَ عَلٰی كُلِّ شَیْئٍ قَدِیْرٌ۔

allaahumma inna haazaa masjedul qiblatayne wa mosallaa nabiyyenaa wa habeebenaa wa sayyedenaa mohammadin sallal laaho a'layhe wa aalehi wa sallama allaahumma innaka qulta wa qawlokal haqqo fee ketaabekal munzale a'laa sadre nabiyyekal mursale: 'qad naraa taqalloba wajhaqa fis-samaaa-e fa-la-nowalleyannaka qiblatan tarzaahaa fa-walle wajhaka shatral masjedil haraame' allaahumma kamaa ballaghtanaa fid dunyaa zeyaaratahu wa maaa-serahush shareefata falaa tohrimnaa yaa allaaho fil aakherate min fazle shafaa-a'te mohammadin sallal laaho a'layhe wa aalhe wa sallama wah-shurnaa fee zumratehi wa tahta lewaaa-ehi wa amitnaa a'laa mahabbatehi wa sunnatehi was-qenaa min hawzehil mawrede be-yadehish shareefate sharbatan hanee-atan maree-atan laa taz-ma-o ba'dahaa abadan innaka a'laa kulle shay-in qadeerun.