ATLANTA (AP) — Most candidates for the state Legislature would love to campaign door-to-door with a former president, but Jason Carter wanted to keep his famous grandfather away for a while.

The grandson of Jimmy Carter wanted to do it on his own, without relying on his famous family name, even though grandma and grandpa have been asking for months to get out on the trail with him. The younger Carter finally relented with a special election for a vacant state Senate seat just days away — and there were Jimmy and Rosalynn Carter, handing out fliers and shaking hands Saturday with surprised residents in a tree-lined Atlanta neighborhood.

‘‘Oh my gosh, President Carter I can’t believe you’re on my front lawn,’’ Christine Marsteller said as Jimmy Carter slowly made his way up to her yard sale.

Yes, Marsteller said, absolutely she would vote for Jason Carter on Tuesday.

‘‘Don’t forget, it’s very important,’’ the 85-year-old Carter said, pecking the 29-year-old Emory University researcher on the cheek with the politician’s practiced ease.

Jason Carter said he didn’t take his grandparents up on their offer sooner because he wanted to prove he could do the hard work on his own. After all, with the Carter name comes high expectations for success.

‘‘I can’t be trading on my family name,’’ the 34-year-old lawyer said in an interview with The Associated Press. ‘‘This is not a campaign of entitlement. We’ve got to earn this on our own.’’

Still, in a special election where turnout will be key, he is rolling out the political royalty to rally voters. He is facing a Democrat, a Libertarian and an independent.

If he wins, Carter would become the first in his family to be elected to political office since his grandfather won the presidency in 1976.

Jimmy Carter served two terms in the Georgia Senate before becoming the state’s governor in 1971.

The heavily Democratic district covers portions of Atlanta and Decatur in DeKalb County and has a large Jewish population, which has resurrected some touchy questions about Jimmy Carter’s strained relationship with the community.

Jimmy Carter outraged many Jews with his 2006 book ‘‘Palestine: Peace Not Apartheid’’ by comparing Israeli treatment of Arabs in the West Bank and Gaza to the legalized racial oppression that once existed in South Africa.

In a sign that emotions on the issue still run high, a flier has circulated in recent days in one Jewish neighborhood that purported to show a Jason Carter donor with the late Palestinian leader Yasser Arafat. Jason Carter called the anonymous flier ‘‘ridiculous and completely false.’’

And there have been some questions about the timing of Jimmy Carter’s apology at the end of last year for any words or deeds that may have upset the Jewish community. The open letter came soon after Jason Carter announced he would seek the state Senate seat.

Jason Carter said the Al Het — or prayer offered on Yom Kippur — had been in the works long before he ever decided to run for office.

Carter’s main opponent, Democrat Tom Stubbs, is a 53-year-old lawyer from Decatur with a long history of civic involvement. Stubbs calls Carter ‘‘a nice young man’’ but suggested he hasn’t paid his dues.

‘‘I’m a strong believer that you sweep the floor before you run the store. I guess we’ll see if the voters agree with that,’’ Stubbs said.

Carter isn’t taking anything for granted, although the name clearly helps.

On a recent weekday he visited the Mack Love Senior Center and interrupted a penny canasta game to introduce himself. The elderly women seem more interested in their cards until one asks, ‘‘any relation to Jimmy Carter?’’

‘‘Yes, he’s my grandfather,’’ Jason answers.

Suddenly, he has their full attention.

Questions ensue about his uncle Billy and his great-grandmother Lillian, both deceased, and Jimmy Carter’s weekly Sunday school classes in Plains, Ga.

‘‘He seems like a very nice young man,’’ 96-year-old Katherine Shaw gushes afterward.