The home side are in third place with four points to their name, while the visitors are two points better off in second position in Group H.
Match preview
Hamilton have returned to the second tier after they beat Alloa Athletic and Inverness Caledonian Thistle in the Scottish Championship playoffs.
However, before they begin their Championship campaign, the Accies will attempt to reach the League Cup knockout rounds for the first time since the 2019-20 season.
They began the 2024-25 edition with a goalless draw against fourth-tier Stirling Albion, before they missed out on the bonus point with a defeat in the subsequent penalty shootout.
However, John Rankin's side produced a stronger performance in Saturday's away game against Stranraer, with Steven Bradley, Kyle MacDonald and Euan Henderson finding the net in a commanding 3-0 victory.
They will now turn their focus to their first meeting with Ross County since prevailing in a penalty shootout in a Scottish Cup tie in January 2023.
Ross County will compete in the Scottish Premiership this season after they retained their top-flight status via the relegation playoffs.
The Staggies claimed a resounding 6-1 aggregate win over Raith Rovers to extend their top-flight stay into a sixth consecutive campaign.
Before they begin their league campaign with an away clash against Motherwell on August 3, Ross County will try to progress to the League Cup knockout rounds for a third consecutive season.
Don Cowie's side have made a promising start to the group phase, recording a 3-1 win over Stranraer before beating Raith Rovers 2-1 in Saturday's home fixture thanks to George Harmon's 87th-minute winner.
The Staggies remain behind group leaders Raith Rovers on goals scored, but a positive result on Tuesday would move them to the top of the standings with one game left to play against Stirling Albion.
Hamilton Academical Scottish League Cup form:
L
W
Ross County Scottish League Cup form:
W
W
Team News
Hamilton defender Fergus Owens will miss the entire 2024-25 season after suffering a knee injury in pre-season.
Ben Williamson was forced off in the first half of Saturday's win over Stranraer, making him an obvious doubt for Tuesday's home fixture.
Kevin O'Hara will offer one of the home side's main goal threats after finishing the 2023-24 season with 20 goals in 45 competitive appearances.
As for the visitors, they are still unable to call upon Will Nightingale and Max Sheaf due to knee and thigh injuries respectively.
Defender Michee Efete is pushing for a starting berth after featuring as a substitute in the two matches against Stranraer and Raith Rovers.
Jordan White has scored three goals in the first two League Cup games, and he will look to continue his fine form when he resumes his forward partnership with Eamonn Brophy.
Hamilton Academical possible starting lineup:
Lyness; MacDonald, Kilday, McGinty, Hendrie; Maguire, Barjonas; Bradley, Shaw, Henderson; O'Hara
Ross County possible starting lineup:
Laidlaw; Efete, Wright, Lamie; Brown, Randall, Loturi, Harmon; Telfer; Brophy, White