I don't know if any of the following are your family or not but they are some that are connected to my family in either Leon or Freestone Counties. You can see if you think any of them are yours.
Male Adams married to Mary Frances Overstreet who died in Freestone County at about the age of 19 before October 1862. Her family came to Freestone County from east Mississippi in the 1850s. Mary Frances was my first cousin 4 times removed.
Male Adams married to Mary Ellen Lee, first cousin to Mary Frances Overstreet. Mary Ellen was born in 1842. Her family came to Leon County from east Mississippi in the late 1860s, then moved to Freestone County after a couple of years. Mary Ellen was my great great grand aunt.
Mary Ellen's brother, John Lee, married Ceatte Adams, daughter J.I. Adams, in 1881. She was his second wife. Ceatte had siblings Follina, Dulca and John. John Lee was my great great grand uncle. John, being Mary Ellen's brother, came with her and the rest of their family (the family of Jacob Walker Lee) to Leon and then Freestone County as described above.
Ceatte's sister, Dulca Adams, married one of John Lee's son by his first wife, John Robert Lee.
Ceatte's other sister, Follina, married another of John Lee's sons by his first wife, James B. Lee.
Ceatte's brother, John Adams, married one of John Lee's daughters by his first wife, Nancy C. Lee.
Fallene Adams married another of the Lee siblings, James Lee, brother of Mary Ellen and John.
Another first cousin of Mary Frances Overstreet, Mary Ellen Lee, John Lee and James Lee was Sarah M. Williamson. She married Jacob J. Adams. Sarah's family came to Freestone County in the 1860s.
Sarah's sister, Mary Williamson, married Peter L. Adams and they had children Cynthia and William Joseph. I do not know if Jacob J. Adams and Peter L. Adams were related but I suspect that they were brothers.
Another first cousin of Mary Frances Overstreet, Mary Ellen Lee, John Lee and James Lee and double first cousin to Sarah M. and Mary Williamson was Margie Eleanor Williamson. She married Jefferson Adams. Again, her family came to Freestone County in the 1850s
I realize that most of these connections seem to relate more to Freestone County than Leon County but those two counties do border each other and there was some movement between them. The main family connection between all of these is the Blakeleys. All of those first cousins mentioned above were first cousins by virtue of sharing common Blakely grandparents. Several Blakely siblings and their families moved to Freestone County in the 1850s and 1860s with one (the Lees, Jacob Walker Lee's wife was a Blakely) moving first to Leon County then on the Freestone County. Several of the Lee family descendants ended up back in Leon County. The fact that so many of these Blakely descendants married Adams people makes me think that these Adams were related also. In fact all four of the children of J.I. Adams married Blakely descendants. I do not know, however, if any of these Adams are related to your Adams.