Clipping the nails is one of the Sunan al-Fitrah, as is indicated by the saheeh ahaadeeth, and it is mustahabb to start on the right, because it is proven in Saheeh al-Bukhaari (163) that ‘Aa’ishah (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) used to like to start on the right when putting on shoes, combing his hair, purifying himself and in all his affairs.
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’ (1/339): There is scholarly consensus that clipping the nails is Sunnah, and that applies equally to men and women, and to the hands and feet. It is mustahabb to start with the right hand, then the left, then the right foot then the left. End quote.
And he (may Allaah have mercy on him) said in Sharh Saheeh Muslim (3/149): It is mustahabb to start with the hands before the feet, and to start with the forefinger of the right hand, then the middle finger, then the ring finger, then the pinkie finger, then the thumbs, then to move to the left hand and start with the pinkie finger then the ring finger, until all the fingers are done, then to move to the right foot and start with the smallest toe on the right foot and end with the smallest toe on the left foot. And Allaah knows best. End quote.
The Hanbalis mentioned a different sequence of fingers when clipping the nails, but no saheeh report has been narrated from the Prophet (peace and blessings of Allaah be upon him) concerning this matter.
Al-‘Iraaqi (may Allaah have mercy on him) said in Tarh al-Tathreeb (2/77): There is no proven hadeeth which may be followed with regard to how to clip the nails. End quote.
Ibn Hajar said in Fath al-Baari (10/345):
There is no proven hadeeth about the order of fingers when cutting the nails. … Ibn Daqeeq al-Eid rejected the order mentioned by al-Ghazaali and those who followed him, and he said: There is no basis for any of that, and to suggest that it is mustahabb when there is no evidence for that is abhorrent in my view. If anyone were to suggest that it is mustahabb to start with the right forefinger because of its honourable status, there is no basis for the rest of this sequence. Yes there is a basis for starting with the right hand and the right foot, which is “he liked to start on the right.” End quote.
And Allaah knows best.