Mahanidhi Madan Gopal Das

Confusion has arisen regarding which fingers to use while chanting Hare Krishna Nama or Diksa Mantras. The clear truth is found in Hari Bhakti Vilasa as follows:

Siva Agama:
andmamadhyamakramya japam kuryyattu manasam madhyama 
madhyama kramya japam kuryyadupamsukam tarjjanirh
tu samakramya japam naiva tu karayet

While chanting manasic japa (silent in the mind), one should hold the beads with the thumb and ring finger.
However, when chanting upamsu (softly), one should hold the beads with the thumb and middle finger. Never use the index finger while chanting  (Hari Bhakti Vilasa 17.114).

tarjjanya na sprset sutram kampayenna vidhiinayet 
angustha parvva madhyastham parivarttam samacaret

Don’t touch index finger to mala while chanting japa.
Don’t swing, rattle or shake beads while chanting.
Use the thumb and middle finger to move from one bead to another. (if you are chanting softly, upamsu japa, Hari Bhakti Vilasa 17.123)

Conclusion: Two ways to chant and both are correct. Thumb and ring finger for silent, mental manasi japa.
(Hari Bhakti Vilasa 17.114);
Thumb and middle finger for soft chanting, upamsu japa.
Hari Bhakti Vilasa 17.114, 123
Nama Acarya Sri Haridas Thakur ki jai! Jai Jai Sri Radhe!