Short answer
After. Jesus lived in the first century, and Prophet Muhammad ﷺ was born in Makkah around 570 CE, roughly six centuries later. Muslims believe no prophet came between them, that Jesus foretold his coming, and that he is the last of the prophets.
That Muhammad ﷺ is the final prophet (khatam al-nabiyyin) is an essential belief of every Muslim, stated in the Quran and agreed upon by all schools. Anyone who claims prophethood after him is rejected by consensus. The return of Jesus near the end of time does not contradict this, as he was a prophet before.
The four schools agree on this.
Explanation
Jesus (Isa) was born to Mary in Palestine at the start of the common era. Prophet Muhammad ﷺ was born in Makkah in about 570 CE, received the first revelation around 610 at the age of forty, and passed away in Madinah in 632. The Companion Salman al-Farisi, who had searched among Christian monks before finding Islam, said the gap between the two was six hundred years. Al-Bukhari records his words.
The Quran calls that gap a fatrah, a period without messengers. The Prophet ﷺ himself said there was no prophet between him and Jesus, and that he is the closest of people to the son of Mary.
The order matters in Muslim belief. Jesus gave good news of a messenger to come after him named Ahmad, one of the names of the Prophet ﷺ. The Quran calls Muhammad ﷺ the seal of the prophets, so no new prophet or scripture comes after him. When Jesus returns before the Last Day, he will follow the shariah of Muhammad ﷺ and bring no new law.
Muslims also do not see Islam as a new religion that began in 610. The same message of worshipping the one God was taught by every prophet. See is Islam older than Christianity, how Muhammad and Jesus are related and Prophet Muhammad.
The evidence
Quran, Surah As-Saff 61:6
وَإِذْ قَالَ عِيسَى ٱبْنُ مَرْيَمَ يَٰبَنِىٓ إِسْرَٰٓءِيلَ إِنِّى رَسُولُ ٱللَّهِ إِلَيْكُم مُّصَدِّقًۭا لِّمَا بَيْنَ يَدَىَّ مِنَ ٱلتَّوْرَىٰةِ وَمُبَشِّرًۢا بِرَسُولٍۢ يَأْتِى مِنۢ بَعْدِى ٱسْمُهُۥٓ أَحْمَدُ ۖ فَلَمَّا جَآءَهُم بِٱلْبَيِّنَٰتِ قَالُوا۟ هَٰذَا سِحْرٌۭ مُّبِينٌۭ ﴿٦﴾
And [mention] when Jesus, the son of Mary, said, "O children of Israel, indeed I am the messenger of Allah to you confirming what came before me of the Torah and bringing good tidings of a messenger to come after me, whose name is Ahmad." But when he came to them with clear evidences, they said, "This is obvious magic."
Jesus foretold a messenger who would come after him.
Quran, Surah Al-Maaida 5:19
يَٰٓأَهْلَ ٱلْكِتَٰبِ قَدْ جَآءَكُمْ رَسُولُنَا يُبَيِّنُ لَكُمْ عَلَىٰ فَتْرَةٍۢ مِّنَ ٱلرُّسُلِ أَن تَقُولُوا۟ مَا جَآءَنَا مِنۢ بَشِيرٍۢ وَلَا نَذِيرٍۢ ۖ فَقَدْ جَآءَكُم بَشِيرٌۭ وَنَذِيرٌۭ ۗ وَٱللَّهُ عَلَىٰ كُلِّ شَىْءٍۢ قَدِيرٌۭ ﴿١٩﴾
O People of the Scripture, there has come to you Our Messenger to make clear to you [the religion] after a period [of suspension] of messengers, lest you say, "There came not to us any bringer of good tidings or a warner." But there has come to you a bringer of good tidings and a warner. And Allah is over all things competent.
The Prophet ﷺ came after a gap with no messengers.
Quran, Surah Al-Ahzaab 33:40
مَّا كَانَ مُحَمَّدٌ أَبَآ أَحَدٍۢ مِّن رِّجَالِكُمْ وَلَٰكِن رَّسُولَ ٱللَّهِ وَخَاتَمَ ٱلنَّبِيِّۦنَ ۗ وَكَانَ ٱللَّهُ بِكُلِّ شَىْءٍ عَلِيمًۭا ﴿٤٠﴾
Muhammad is not the father of [any] one of your men, but [he is] the Messenger of Allah and last of the prophets. And ever is Allah, of all things, Knowing.
Muhammad ﷺ is the final prophet.
Sahih al-Bukhari 3442
Sahih... أنا أولى الناس بابن مريم والأنبياء أولاد علات ليس بيني وبينه نبي ...
"I am the closest of people to the son of Mary. The prophets are brothers by one father, and there was no prophet between me and him."
No prophet came between Jesus and Muhammad ﷺ.
Where the ruling is recorded
- al-Aqida al-Tahawiyya, the section on the Prophet ﷺ as the seal of the prophets. Every claim of prophethood after him is false.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.