The Great-Grandfather of Imaam Bukhaari (rahimahullah):

The name of the great-grandfather of Imaam Bukhaari (rahimahullah) was Mugheerah. He was initially a fire worshipper. However, Allah Ta‘ala blessed him with imaan. He thus embraced Islam at the hands of Yamaan Ju’fi. (Siyar A’laam min Nubalaa 12/392)

It is on account of the great-grandfather of Imaam Bukhaari (rahimahullah) accepting Islam at the hands of Yamaan Ju’fi, the governor of Bukhaara, that Imaam Bukhaari (rahimahullah) is also referred to as “Al-Ju’fi”. (Hadyus Saari pg. 477)

The Father of Imaam Bukhaari (rahimahullah):

The name of the father of Imaam Bukhaari (rahimahullah) was Ismaa‘eel. He passed away while Imaam Bukhaari (rahimahullah) was still a young child. Hence, Imaam Bukhaari (rahimahullah) was raised by his mother. (Hadyus Saari pg. 477)

Ismaa‘eel was a pious and saintly personality who was among the great Muhadditheen of his era. He was the student of Imaam Maalik (rahimahullah) and Imaam Hammaad bin Zaid (rahimahullah). He was also blessed with the good fortune of meeting Hazrat ‘Abdullah bin Mubaarak (rahimahullah). (Hadyus Saari pg. 477)

Regarding his piety, Ahmed bin Hafs (rahimahullah) mentions:

I came to visit Ismaa‘eel, the father of Imaam Bukhaari (rahimahullah), at the time when he was on his deathbed. While lying on his deathbed, he said, “I do not know of a single dirham, in my wealth, which was earned from haraam sources, or even from doubtful sources.” (Hadyus Saari pg. 479)

It was on account of Imaam Bukhaari (rahimahullah) being nurtured and raised with the pure, halaal earnings of his father that Allah Ta‘ala blessed him with such acceptance in deen and made him the Imaam of Hadith in the world.