I will show the relationship between Siddhi, Siddha and Siddiqui.
In India, siddha are perfect Yogis. The first principle of 8-steps Yoga is Yama which also has Satya or Truthfulness. It is abbreviated form of siddha-ka for male and siddha-kA for female. Siddhi are powers attained in the path of Yoga.
Mohammad's wife Aisha, daughter of Abu Bakr. was called al-siddiqa bint al-siddiq,
The descendants of Abu Bakr are called Siddiqui but later it may have been abused to indicate a great power bearer and false origins. Mohammad was also called al-saddiq.
"al" is a definitive article like "the".
She is called the siddhi-kA daughter of the siddhi-ka (of Abu Bakr) or the truthful woman, daughter of the truthful man.
The adjective truthful also means perfect.
The sound "a" and "A" or "aa" are very confusing, and hence Ram, KrishN and Yog become Rama, Krishna and Yoga
