Praise be to Allah.
The Sunnah is for the Muslim to count his tasbeeh and tahleel on his fingers, because of the report narrated by Ahmad (25841) and Abu Dawood (1501) from Humaydah bint Yaasir, from Yaseerah who told her: The Prophet (blessings and peace of Allah be upon him) instructed them to pay attention what reciting takbeer, taqdees and tahleel, and to count on their fingers, for they (the fingers) will be questioned and made to speak.
Classed as hasan by al-Albaani in Mishkaat al-Masaabeeh, no. 2316.
What is meant by the phrase “they (the fingers) will be questioned and made to speak” is that they will testify to that effect. This was stated by al-Mubaarakfoori.
However, there is nothing wrong with reciting tasbeeh and dhikr, and remembering Allah, may He be exalted, by any permissible means, such as using the masbahah (“prayer beads”) and, similarly, the tasbeeh ring and other progammed devices which one may use to help keep track, because they come under the principle that the means are subject to the same ruling as the ends. If a person intends good by using this means, he will have what he intended.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
With regard to counting it with date stones and pebbles and the like, that is fine and some of the Sahaabah (may Allah be pleased with them) used to do that. The Prophet (blessings and peace of Allah be upon him) saw the Mother of the Believers counting tasbeeh with pebbles and he approved of her doing that; it was also narrated that Abu Hurayrah counted tasbeeh with pebbles.
With regard to (counting tasbeeh) with beads put together on a string, some of the scholars regarded it as makrooh and some of them did not. If the intention behind it is good, then it is good and is not makrooh.
But as for using it when there is no need to do so, or making it visible to people, such as hanging it around the neck or wearing it like a bracelet on the wrist, and the like, this is either showing off to people or gives rise to suspicion that one is showing off, and is resembling the show-offs unnecessarily. The former is haraam and the least that can be said about the latter is that it is makrooh.
End quote from Majmoo‘ al-Fataawa (22/506)
For more information, please see the answers to questions no. 3009, 140127 and 139662
And Allah knows best.