El Chapo's life in lock-up is apparently getting lonely -- 'cause now he's asking a judge to let his wife visit him in prison ... and for his young daughters to be able to give him a ring.

The notorious Mexican cartel kingpin is begging a NYC court to authorize a family visit at the supermax United States Penitentiary Florence in Colorado -- where he's spending the rest of his life behind bars.

That's not all ... the ex-drug lord is also asking the court to continue allowing him 2 15-minute calls a month with his girls -- whom he got cut off from last May, which he suggests is the doing of the feds because he's trying to have his case tossed, and he believes they're retaliating.

Chapo writes of the prosecutor in his case, "She was surely upset because in the pro se motion, I exposed the inefficiency of the lawyers who did not fight the anomalies of the prosecutors throughout the process."

He adds, "And in response, they have decided to punish me by not letting me talk to my daughters. To this day they have not told me if they will no longer give me calls with my girls. That's why I'm bothering you, since you authorized those two calls a month. That is why I ask for your intervention, since it is unprecedented discrimination against me."

He goes on to say this is the only way to communicate with his kids, since they live in Mexico ... and can't visit him here in the States without a visa, which they don't currently have.

Chapo goes on to say the only person who could theoretically come and visit him in person would be his wife Emma Coronel -- and he's asking the court to give her the green light to do so. He doesn't mention a conjugal visit here ... but, well, y'know.

Funny enough ... Chapo signs this letter himself, and it sounds like he wrote it in his own words too. So, this clearly means a lot to him ... and he's writing in English to boot.

Emma herself was also behind bars for a bit -- that is, until she got released from prison last year ... and she's been living in L.A. ever since. You'll recall ... Emma hit the town and partied shortly after she was sprung.

As we reported ... El Chapo was found guilty back in 2019 for engaging in a continuing criminal enterprise, conspiracy to launder narcotics proceeds, international distribution of cocaine, heroin, marijuana, and other drugs, and use of firearms.

Of course, this came after the Sinaloa Cartel's leader was captured by the Mexican government in 2014 before famously escaping from jail cell more than a year later through a mile-long underground tunnel -- only to be caught again in early 2016.