Devi Bhagavatam mentions some results in Book 11 for applying Urdhva Pundra (Tilak worn by Vishnu Devotees) with different fingers.
According to the chapter,
Thumb : Nourishment is obtained
Middle Finger : Longetivity is increased
Ring Finger : Food is obtained
Forefinger : Liberation is obtained
Below is an excerpt of Chapter 15:
If the Ûrdhapundra be drawn by the thumb, nourishment is obtained; if it be drawn by the middle finger, longevity is increased; if it be drawn by nameless or ring finger, food is obtained and if it be drawn by the fore finger, liberation is attained. So the Ûrdhapundras ought to be drawn by these fingers, only be careful to see that the nails do not touch at the time of making the mark.
In the beginning of the chapter, Lord Vishnu also says how the sacred ashes (Bhasma) are to be applied. While applying fore, middle and ring fingers of the right hand fingers are used.
One is to hold the Tripundra, six Angulas high or greater by the fore, middle and ring fingers of the right hand. If anybody uses Tripundra, shining and brilliant, and extending from eye to eye, he becomes, no doubt, a Rudra. The ring-finger is the letter “A,” the middle finger is “U” and the forefinger is “M”;
But I have observed that elders and some priests mostly instruct us to apply tilak with three fingers viz Ring finger, Middle finger and thumb and not the index finger and little finger.