Can't help very much. Let's start with background info. Samuel was in Lowndes Co, GA in 1840; in Levy Co, FL in 1860 on. He had 8 sons: Andrew Jackson; Thomas Newman; James Monroe; William Washington; Samuel Madison; Jasper J; Montgomery Newton; Marion Franklin.
In the 1850 slave schedule James had one female in Lowndes Co and Samuel had 37 in Levy Co, 3-3yr old males and 2-2yr old males.
In the 1860 slave schedule Andrew has 8, 1 male 4. Thomas has 6, 1 male 17, 1 male 1. Samuel has 56, 7 in the age group you show. There are several Jackson slaveholders, none in Levy Co. If the info is correct then we're looking for a male born in FL.
In 1870 there are 8 Hannah's in Levy, none with sons the right age. There are 3 Berry's, no fits. One black 'B' from PA. Only 22 black males in total.
There are no Clyatts that fit that description in any of the census records.
1n 1880 there is in Levy Co a Cary Jackson, 30 with wife Hannah, 24.
In 1900 no Jacksons that I could twist to make fit.
Donald