Roger Clemens of the New York Yankees pitches against the Pittsburgh Pirates, June 9, 2007, at Yankee Stadium in New York City. Kathy Willens/AFP/Getty Images

A Twitter feud between Roger Clemens and Roy Halladay continued Thursday as the former MLB All-Star pitchers bickered at one another across social media. The argument, which began the day before, is centered on the Hall of Fame and the use of performance-enhancing drugs.

The back-and-forth started when former Philadelphia Phillie and Toronto Blue Jay Halladay took to Twitter to express his satisfaction that former San Francisco Giant Barry Bonds and former New York Yankee and Houston Astro Clemens — both of whom have long been at the center of performance enhancing drug (PED) allegations — did not meet the vote threshold Wednesday to gain entrance in the baseball Hall of Fame.

Halladay said he felt this was deserved, writing on Twitter Wednesday, "When you use PEDs, you admit your [sic] not good enough to compete fairly! Our nations [sic] past time [sic] should have higher standards! No Clemens, no Bonds!"

Clemens was accused of performance-enhancing drug use in baseball's Mitchell Report and in 2008 Brian McNamee, a former New York City police officer and strength and conditioning coach, testified he injected Clemens with steroids. Clemens, 53, has steadily denied PED use and was acquitted in a federal perjury trial relating to testimony on the subject before Congress in 2008. Clemens, who won a record seven Cy Young awards, which are given annually the best pitchers in each of the MLB's two leagues, threw a very thinly veiled barb back at Halladay Wednesday.

"What is disheartening is getting call or text from family or friends about an ill-informed player making an asinine statement. The latest coming from a former Blue Jays pitcher," Clemens, who also played for Toronto, said in a statement to Houston’s KRIV-TV. "Just to enlighten him, he was accused of using amphetamines by our 'strength coach.' You should be careful when putting tweets out while not having facts on the matter at hand."

Clemens appeared to accuse Halladay of using amphetamines as a performance-enhancer, referencing a time when McNamee served as a strength coach for the Blue Jays when Halladay made his way into the league in 1998. Most stimulants weren't banned until 2006, and by that time, Halladay and McNamee had both moved on, according to USA Today. Halladay has also never before been publicly accused of using PEDs, amphetamines or otherwise, NBC Sports' Craig Calcaterra noted.

The former Blue Jay, 38, responded to Clemens Thursday with a simple tweet reading, "I'll let my reputation speak for itself." Halladay, who won two Cy Young awards and retired in 2013, will be eligible for Hall of Fame voting starting in 2019 and is believed by many to have a solid resume.