The Prophet ﷺ said, "Faith (Belief) consists of more than sixty branches (i.e. parts). And Haya (This term "Haya" covers a large number of concepts which are to be taken together; amongst them are self respect, modesty, bashfulness, and scruple, etc.) is a part of faith."  

عَنِ النَّبِيِّ ﷺ قَالَ الإِيمَانُ بِضْعٌ وَسِتُّونَ شُعْبَةً وَالْحَيَاءُ شُعْبَةٌ مِنَ الإِيمَانِ  

that once Messenger of Allah ﷺ passed by an Ansari (man) who was admonishing his brother regarding Haya'. On that Messenger of Allah ﷺ said, "Leave him as Haya' is a part of faith." (See Hadith 9)  

أَنَّ رَسُولَ اللَّهِ ﷺ مَرَّ عَلَى رَجُلٍ مِنَ الأَنْصَارِ وَهُوَ يَعِظُ أَخَاهُ فِي الْحَيَاءِ، فَقَالَ رَسُولُ اللَّهِ ﷺ: «دَعْهُ، فَإِنَّ الْحَيَاءَ مِنَ الإِيمَانِ۔»  

the Prophet ﷺ said, "Ḥayāʾ (modesty) brings about nothing except good."

Thereupon Bushayr b. Kaʿb said: It is written in ˹my˺ wisdom ˹notes˺ that Ḥayāʾ leads to solemnity; Ḥayāʾ leads to tranquility. ʿImrān said to him: I am narrating to you the saying of Messenger of Allah ﷺ and you are speaking about your ˹notes on˺ paper (wisdom book)?  

قَالَ النَّبِيُّ ﷺ «الْحَيَاءُ لاَ يَأْتِي إِلاَّ بِخَيْرٍ۔»

فَقَالَ بُشَيْرُ بْنُ كَعْبٍ: مَكْتُوبٌ فِي الْحِكْمَةِ، إِنَّ مِنَ الْحَيَاءِ وَقَارًا، وَإِنَّ مِنَ الْحَيَاءِ سَكِينَةً۔ فَقَالَ لَهُ عِمْرَانُ: أُحَدِّثُكَ عَنْ رَسُولِ اللَّهِ ﷺ وَتُحَدِّثُنِي عَنْ صَحِيفَتِكَ؟