(CNN) A Georgia man was executed Wednesday for a 1994 murder after courts denied appeals involving pleas for new DNA testing and a witness's claim that a different man confessed.

Ray Jefferson Cromartie, 52, was convicted of malice murder in the death of convenience store clerk Richard Slysz. The shooting happened while Cromartie and another man tried to steal beer in Thomas County, near the Georgia-Florida state line, authorities said.

Cromartie, who claimed he didn't kill Slysz, died by lethal injection Wednesday night at a prison in Jackson.

Courts denied numerous appeals. The US Supreme Court on Wednesday rejected two requests to stop the execution.

Among Cromartie's requests was for new DNA testing of evidence that his lawyers claimed might show he wasn't the shooter. They asked for testing on clothing and shell casings, the Atlanta Journal-Constitution reported

In a statement published by the newspaper, Cromartie's attorney Shawn Nolan said it was sad and outrageous that Georgia executed his client "after repeatedly denying his requests for DNA testing."

"In this day and age, where DNA testing is routine, it is shocking that Georgia decided to end this man's life without allowing us, his attorneys, access to the materials to do these simple tests," Nolan's statement reads.

Cromartie's brother, Anthony, told CNN affiliate WXIA that his family will continue pushing for DNA testing, hoping to prove Cromartie's innocence. The interview happened Wednesday evening, after he learned the US Supreme Court declined to stop the execution.

"I'm fighting for my brother to show that he did not commit this crime," he told WXIA. "We are going to find out what is the real truth and take it back to court and ensure that my brother's name is proven not guilty of the crime."

Authorities had said Cromartie shot Slysz while he and another man robbed the store in April 1994, and that a different man served as a getaway driver. Both of Cromartie's co-defendants were sentenced to prison and have since been released, WXIA reported

The driver recently said in a court filing that he'd overheard the other robber claim that he, not Cromartie, shot Slysz. State officials argued the new claim didn't matter because the driver didn't see the shooting, the AJC reported

Slysz's daughter, Elizabeth Legette, had supported Cromartie's request for DNA testing, the AJC reported.

"In the course of the past few months, I have not been treated with fairness, dignity, or respect, and people in power have refused to listen to what I had to say," Legette said in a statement released Tuesday, according to the AJC. "I believe this was, in part, because I was not saying what I was expected to say as a victim."