By the close of a day of fluctuating fortunes, the home side were 171 for seven in their second innings, leading by only 133. Claydon added three for 30 to his first innings figures of five for 46, well supported by Darren Stevens (two for 34) and fellow seamers Harry Podmore and Matt Milnes.
In a match yet to feature a half-century from any batsman, Steve Davies (39) and Tom Abell (30) gave Somerset a modicum of hope before George Bartlett (35 not out) and Craig Overton (27 not out) counter-attacked with an unbroken stand of 60.
But the home bowlers still look set to face a stiff task tomorrow in a game most expected last season’s First Division runners-up to win.
The day began with Kent 81 for two in their first innings in reply to 171. They found the going tough under overcast skies, which necessitated the use of Somerset’s new floodlights, against a home attack stepping up on their efforts of the previous day.
Josh Davey and Lewis Gregory bowled tight opening spells, Davey having Sean Dickson caught at first slip for 43 and Gregory picking up the prized wicket of former team-mate Matt Renshaw, taken at mid-off from a leading edge for five.
Heino Kuhn made 18 before having his middle stump uprooted by Craig Overton, Alex Blake played on to Gregory attempting to cut and Daniel Bell-Drummond, who battled hard for his 33 was well caught above his head by Marcus Trescothick at second slip to give Gregory a third victim.
It was 172 for seven at lunch and the afternoon session saw the addition of 37 valuable runs before Kent were bowled out for 209, a handy lead of 38.
That looked an even more advantageous position when Somerset’s top order failed again, Trescothick, Azhar Ali and James Hildreth contributing just nine runs between them as veteran Stevens wielded magic with the new ball, claiming two for 13 from seven overs.
It was 32 for four when Eddie Byrom, on 14, edged Milnes to diving wicketkeeper Ollie Robinson and, although Davies and Abell added 58 with reasonable comfort, both departed to forgettable shots.
Abell was caught behind off a flashing drive to give Claydon his first wicket of the innings and the experienced paceman then bowled Davies off an inside edge to leave Somerset 103 for six, a lead of only 65.
When Gregory was bowled pushing forward to Claydon it seemed Kent had broken the back of the Somerset batting. But 21-year-old Bartlett and England all-rounder Overton had other ideas.
They added 60 in entertaining fashion as the post tea session was played in the best weather of the game.
Kent’s Darren Stevens said: “It’s hard to say what a par score will be in the final innings, but we have talked about taking quick wickets in the morning. We would be happy to chase anything up to 180, but even if the target ended up being 230 we would have a decent chance.
“Beating the team who finished runners-up in the Championship last season would be a tremendous boost for us. But it is only one game and this season is going to be a learning process for us.
“We are a very young team with a couple of old heads to hold things together. The ball is coming out nicely for me. I managed to get Marcus Trescothick with one that swung and James Hildreth with one that seamed so I’m happy with that.”
Somerset skipper Tom Abell said: “We bowled really well today, but unfortunately we have not been anything like our best with the bat in this game and that has given us a lot of work to do.
“George Bartlett and Craig Overton have kept us in the game with their stand at the end of the day and we need to build on that tomorrow. Last season we managed to dig ourselves out of some tough positions and I am looking for the same here.
“The pitch will continue to do a bit for the bowlers and all results are still possible.”