Salat Witr is prayed after Salat Taraweeh and Salat Isha in mosque. This the routine followed in the month of Ramadan in my country. If I wake up early and then pray for Tahajjud, Is it okay?
I hear that Salat Witir is a cover of Salat, so we can't continue another Salat and then do Witir again, may be because the count of the rakaat must be odd.
When you pray in the mosque you have two -good- options:
1) pray witr with the Imam and if you can do the tahajjud later you do it without repeating the witr because it is narrated (there are no 2 witrs in one nights لا وتران في ليلة). And according to the comment in Sunan at-Tirmidhi (see the long Arabic text in the posted hadith below) this is the opinion of Imam Malik, Imam Shafi'i, Imam Ahmad, Imam ibn al-Mubartak and Sufyan ath-Thawry and the scholars of al-Kufa!
Qais bin Talq bin Ali narrated that : his father said: I heard Allah's Messenger saying: "There are no two Witr in one night."
(Sunan at-Thirmidi)
حَدَّثَنَا هَنَّادٌ، حَدَّثَنَا مُلاَزِمُ بْنُ عَمْرٍو، حَدَّثَنِي عَبْدُ اللَّهِ بْنُ بَدْرٍ، عَنْ قَيْسِ بْنِ طَلْقِ بْنِ عَلِيٍّ، عَنْ أَبِيهِ، قَالَ سَمِعْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ " لاَ وِتْرَانِ فِي لَيْلَةٍ " . قَالَ أَبُو عِيسَى هَذَا حَدِيثٌ حَسَنٌ غَرِيبٌ . وَاخْتَلَفَ أَهْلُ الْعِلْمِ فِي الَّذِي يُوتِرُ مِنْ أَوَّلِ اللَّيْلِ ثُمَّ يَقُومُ مِنْ آخِرِهِ فَرَأَى بَعْضُ أَهْلِ الْعِلْمِ مِنْ أَصْحَابِ النَّبِيِّ صلى الله عليه وسلم وَمَنْ بَعْدَهُمْ نَقْضَ الْوِتْرِ وَقَالُوا يُضِيفُ إِلَيْهَا رَكْعَةً وَيُصَلِّي مَا بَدَا لَهُ ثُمَّ يُوتِرُ فِي آخِرِ صَلاَتِهِ لأَنَّهُ " لاَ وِتْرَانِ فِي لَيْلَةٍ " . وَهُوَ الَّذِي ذَهَبَ إِلَيْهِ إِسْحَاقُ . وَقَالَ بَعْضُ أَهْلِ الْعِلْمِ مِنْ أَصْحَابِ النَّبِيِّ صلى الله عليه وسلم وَغَيْرِهِمْ إِذَا أَوْتَرَ مِنْ أَوَّلِ اللَّيْلِ ثُمَّ نَامَ ثُمَّ قَامَ مِنْ آخِرِ اللَّيْلِ فَإِنَّهُ يُصَلِّي مَا بَدَا لَهُ وَلاَ يَنْقُضُ وِتْرَهُ وَيَدَعُ وِتْرَهُ عَلَى مَا كَانَ . وَهُوَ قَوْلُ سُفْيَانَ الثَّوْرِيِّ وَمَالِكِ بْنِ أَنَسٍ وَابْنِ الْمُبَارَكِ وَالشَّافِعِيِّ وَأَهْلِ الْكُوفَةِ وَأَحْمَدَ . وَهَذَا أَصَحُّ لأَنَّهُ قَدْ رُوِيَ مِنْ غَيْرِ وَجْهٍ أَنَّ النَّبِيَّ صلى الله عليه وسلم قَدْ صَلَّى بَعْدَ الْوِتْرِ .
2) pray with the Imam and when he does the salam in witr continue and add another rak'a, then do tahajjud and witr afterwards.
There's a third option which might not be that recommended (as one should follow the imam) if the imam of taraweeh prays witr many people don't perform tasleem after the last raka'a and add an an addional raka'a when the imam finishes witr so that they might pray witr later.
Addition:
If you prayed alone you can still pray witr right before fajr!
