Is there any sahih hadith related to performing Namaz-e-Janaza for one who committed suicide?
Yes it is.
Allah mentions in the Quran, the people for whom funeral is not allowed:
وَلَا تُصَلِّ عَلَىٰ أَحَدٍ مِّنْهُم مَّاتَ أَبَدًا وَلَا تَقُمْ عَلَىٰ قَبْرِهِ ۖ إِنَّهُمْ كَفَرُوا بِاللَّهِ وَرَسُولِهِ وَمَاتُوا وَهُمْ فَاسِقُونَ
And do not pray over any of them who has died - ever - or stand at his grave. Indeed, they disbelieved in Allah and His Messenger and died while they were defiantly disobedient (fasiq).
It logically follows that it is permissible to pray the funeral for anyone who is a Muslim and not a Kafir and a Fasiq but has committed sins that are less than that.
إِنَّ اللَّهَ لَا يَغْفِرُ أَن يُشْرَكَ بِهِ وَيَغْفِرُ مَا دُونَ ذَٰلِكَ لِمَن يَشَاءُ ۚ وَمَن يُشْرِكْ بِاللَّهِ فَقَدِ افْتَرَىٰ إِثْمًا عَظِيمًا
Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. And he who associates others with Allah has certainly fabricated a tremendous sin.
Although it should be obvious that a suicidee is not automatically a disbeliever and may be forgiven, the following hadith is narrated in Sahih Muslim under the title باب الدليل على ان قاتل نفسه لا يكفر (The Chapter: Evidence that the one who kills himself is not considered a disbeliever):
ان الطفيل بن عمرو الدوسي، اتى النبي صلى الله عليه وسلم فقال يا رسول الله هل لك في حصن حصين ومنعة - قال حصن كان لدوس في الجاهلية - فابى ذلك النبي صلى الله عليه وسلم للذي ذخر الله للانصار فلما هاجر النبي صلى الله عليه وسلم الى المدينة هاجر اليه الطفيل بن عمرو وهاجر معه رجل من قومه فاجتووا المدينة فمرض فجزع فاخذ مشاقص له فقطع بها براجمه فشخبت يداه حتى مات فراه الطفيل بن عمرو في منامه فراه وهييته حسنة وراه مغطيا يديه فقال له ما صنع بك ربك فقال غفر لي بهجرتي الى نبيه صلى الله عليه وسلم فقال ما لي اراك مغطيا يديك قال قيل لي لن نصلح منك ما افسدت . فقصها الطفيل على رسول الله صلى الله عليه وسلم . فقال رسول الله صلى الله عليه وسلم " اللهم وليديه فاغفر "
It is narrated on the authority of Jabir that Tufail son of Amr al-Dausi came to the Apostle (ﷺ) and said:
... When the Apostle (ﷺ) migrated to Medina, Tufail son of Amr also migrated to that place, and there also migrated along with him a man of his tribe.
But the climate of Medina did not suit him, and he fell sick. He felt very uneasy. So he took hold of an iron head of an arrow and cut his finger-joints. The blood streamed forth from his hands, till he died.
Tufail son of Amr saw him in a dream. His state was good and he saw him with his hands wrapped.
He (Tufail) said to him: What treatment did your Allah accord to you?
He replied. Allah granted me pardon for my migration to the Apostle (ﷺ).
He (Tufail) again said: What is this that I see you wrapping up your hands?
He replied: I was told (by Allah): We would not set right anything of yours which you damaged yourself.
Tufail narrated this (dream) to the Messenger of Allah (ﷺ).
Upon this he prayed: O Allah, grant pardon even to his hands.
The above is evidence that the Prophet prayed for a person who had killed himself.
Now, regarding the funeral prayer for such a person: There exists a hadith which says that the Prophet didn't offer funeral for a person who had killed himself:
عن جابر بن سمرة، قال اتي النبي صلى الله عليه وسلم برجل قتل نفسه بمشاقص فلم يصل عليه
Jabir b. Samura reported:
(The dead body) of a person who had killed himself with a broad-headed arrow was brought before the Messenger of Allah (ﷺ), but he did not offer prayers for him.
عن جابر بن سمرة، ان رجلا، قتل نفسه بمشاقص فقال رسول الله صلى الله عليه وسلم " اما انا فلا اصلي عليه " .
Narrated from Jabir bin Samurah that: a man killed himself with an arrowhead and the Messenger of Allah said: "As for me, I will not pray for him."
The Prophet's words اما انا فلا اصلي عليه (As for me, I will not pray for him) shows that the Prophet didn't offer the funeral himself but the Sahabah did, and the Prophet didn't forbid them nor declared a funeral invalid ... hence it is permitted and what the Prophet did with himself was to show his displeasure with the act.
This is analogous to the case of a person who died without settling his debts, and the Prophet didn't offer his funeral but told the Sahabah to offer it:
ثم اتي بجنازة اخرى، فقال " هل عليه من دين ". قالوا نعم. قال " صلوا على صاحبكم ". قال ابو قتادة على دينه يا رسول الله. فصلى عليه.
Another dead person was brought and he asked, "Is he in debt?" They said, "Yes." He (refused to lead the prayer and) said, "Lead the prayer of your friend." Abu Qatada said, "O Allah's Messenger (ﷺ)! I undertake to pay his debt." Allah's Messenger (ﷺ) then led his funeral prayer.
Below are some relevant excerpts on the views of the Sunni schools on the matter:
من قتل نفسه ولو عمدا يغسل ويصلى عليه به يفتى
And the person who kills himself, even if intentionally, then he shall be bathed and the funeral will be prayed and this is the fatwa on this.
ويصلى على قاتل نفسه
Funeral Prayer will be offered for one who kills himself.
وأجمع المسلمون على أنه لا يجوز ترك الصلاة على جنائز المسلمين ، من أهل الكبائر كانوا أو صالحين ، وراثة عن نبيهم صلى الله عليه وسلم قولا وعملا . والحمد لله . واتفق العلماء على ذلك إلا في الشهيد كما تقدم ; وإلا في أهل البدع والبغاة
And the Muslims have a consensus that it is not valid to refuse the funeral of a Muslim, be they those who have committed major sins or be they righteous and this is proven from the Prophet's sayings and actions. Praise be to Allah. And the Ulema are agreed on this except for the case of a Martyr, an Innovator (Ahle Biddah) and Rebels.
قال الحسن والنخعي وقتادة ومالك وأبو حنيفة والشافعي وجماهير العلماء : يصلى عليه
The saying of Hasan, Nakhni, Qatadah, Malik, Abu Hanifa, Shafi and the majority of the ulema is: The funeral prayer will be offered for him (one who kills himself)