Tom Brady has the most career passing touchdowns on 3rd down, with 182 touchdowns.

most touchdown passes on third down
Interpreted as:
most touchdown passes by a player on third down
BradyBreesManningRiversRodgersRoethlisbergerManningRyanPalmerStaffordFavreFlaccoCutlerWilsonRomoFitzpatrickDaltonNewtonCousinsCarrHasselbeckSmithWarner182164144136128127121107998580757267656564636058585757
NAMEGPTDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Tom BradyTom Brady3011821,5632,66058.819,5517.465.06.8622.31691,04894.8
Drew BreesDrew Brees2861641,7122,66664.220,7977.872.76.2762.912293696.7
Peyton ManningPeyton Manning2341441,3372,14762.315,3177.165.56.7733.47855091.9
Philip RiversPhilip Rivers2421361,3462,23860.117,5587.872.66.1894.011470088.6
Aaron RodgersAaron Rodgers1951281,0241,68660.714,6988.775.47.6352.1119728105.7
Ben RoethlisbergerBen Roethlisberger2331271,3182,13661.716,8557.972.35.9663.11881,30193.3
Eli ManningEli Manning2351211,2952,27556.916,2417.169.15.3863.812789581.2
Matt RyanMatt Ryan2051071,2602,00163.015,2257.674.35.3422.19462495.3
Carson PalmerCarson Palmer181991,0721,81359.112,4786.968.95.5583.211380484.9
Matthew StaffordMatthew Stafford165859781,69057.912,3597.374.95.0583.46543683.2
Brett FavreBrett Favre173809741,64159.411,9567.369.14.9654.09767581.6
Joe FlaccoJoe Flacco176759891,72357.411,7946.867.04.4492.812184681.1
Jay CutlerJay Cutler153727881,34658.59,4507.061.85.3564.210970680.6
Russell WilsonRussell Wilson144677121,18859.98,8677.561.65.6262.26038892.8
Tony RomoTony Romo130656791,12760.28,8477.968.15.8363.29666390.9
Ryan FitzpatrickRyan Fitzpatrick162657711,36656.49,0656.656.04.8493.68751177.7
Andy DaltonAndy Dalton143647181,28555.98,6076.760.25.0423.35127979.5
Cam NewtonCam Newton140636101,10855.17,7767.055.55.7423.87662980.4
Kirk CousinsKirk Cousins1086060897562.47,1117.365.86.2272.8154293.4
Derek CarrDerek Carr110586431,06960.18,0517.573.25.4222.12418393.1
Matt HasselbeckMatt Hasselbeck172587931,39556.89,4756.855.14.2473.41531,02777.6
Alex SmithAlex Smith173578351,43758.19,4656.654.74.0392.713175479.9
Kurt WarnerKurt Warner1055754087361.96,4707.461.66.5303.48354492.0
Donovan McNabbDonovan McNabb154567411,34655.19,0086.758.54.2352.61511,01178.9
Daunte CulpepperDaunte Culpepper1035551886559.96,9398.067.46.4313.69051091.7
StatMuse has event-level data for passing touchdowns going back to the 2000 season.

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