Griffith and Griffiths as surnames in the UK are very common, in some areas of England and Wales (possibly Scotland and Ireland (Northern and the Republic) too) it's almost impossible to research a particular line because so many "unrelated" people with the surname lived there. It's easier if you have some details to go on.
In the 1930 U.S. Census, Bergholz, Jefferson Co. OH, page 8A:
Bryon Griffith, age 34, Coal Miner, married at age 24, Born in OH, both parents born in OH
Hazel Griffith, age 26, married at age 18, Born in OH, Both parents born in West Va.
William M. Griffith, age 6, born in OH
Donna J. Griffith, age 3-3/12, born in OH
Emogene Griffith, age 12, born in OH
Same page but 2 households away:
Joseph Griffith, age 38, Coal Miner, married at age 18, born in OH, both parents born in Oh
If you'd like me to email you an image of the census page, contact me at my D-mail address and provide your regular email address. I suspect that Bryon and Joseph are brothers. Since Bryon was born in Ohio, you should be able to find him with his parents in earlier censuses in Ohio to confirm that. Censuses were taken every 10 years. This is the easiest method to trace your family back in time.