In Summerhall's Royal Dick Bar, two fierce (and accidentally colour co-ordinated) theatremakers are discussing their respective shows at the venue for the Fringe. It's the first time they've met each other, but there is an instant rapport between these articulate young artists. Both create work which defies easy genre, but has the immediacy of live art.

Leyla Josephine, bringing her new show Daddy Drag to Edinburgh, is a spoken word performer based in Glasgow and Harry Clayton-Wright, currently based in Brighton, mostly performs queer cabaret, having toured with Briefs, but is flying solo this year with Sex Education.

Leyla Josephine: This is my second solo show. I'm a spoken word performer and poet by trade, but I studied contemporary theatre. This doesn't have any spoken word in it. It's about my dad, my relationship to him and in order to try and understand him, I become an archetype of a dad. I do it in drag. My dad died, so it's been a grim process in some ways. But although it's dark in places, there's a lot of heart. It's quite funny and silly as an experience. My mum features in recordings too.

Harry Clayton-Wright: Mine is about how we learn about sex and how it shapes us later in life. My mum didn't speak to me about sex whatsoever, but when I was 14, my dad bought me some gay porn DVDs. So I decided to interview my mum, and that conversation plays throughout the show. I found the porn recently, under my bed, so the audience can see the porn I was exposed to, watching as a kid. I also delve into my sexual history – good, bad and everything in-between – and it tries to link it altogether, and work out how it all sits and it's funny and moving. I found out stuff about my mum and dad's relationship that I didn't know.

LJ: Did you want to know?!

HC-W: Yeah, it's fascinating. My mum hadn't asked any of the questions beforehand. You hear me finding out this for the first time. It's very explicit, quite full-on.

LJ: A true juxtaposition.

HC-W: Yeah. My mum and I have got closer through the experience.

LJ: Can she see it [the show]?

HC-W: She can't ever see it. It's too … it goes quite far. All my family are banned from seeing it!

LJ: Me and my mum went on a total journey with it. One of the reasons I am in drag is that I found some drag clothes of my dad so that got us on the step to making a drag show and there were no answers around it. We don't know if it was a sex thing, or a costume thing. My mum has no idea.

Harry Clayton-Wright / credit: Holly Revell

HC-W: The ethics of working with a parent come into it, and you want them to feel comfortable.

LJ: Yeah, what does that mean for the family – whose story is it to tell? Everyone has their own version of the truth, it's a thin wire. You have to be considerate. My mum was great, she was never going to stop it.

HC-W: It was exactly the same for me, I went through that. How do you deal with it?I feel she enriched it, made it a fuller picture.

LJ: You're trying to fit a situation into a show. What was your technique for creating it?

HC-W: I amassed a lot of research. Had to whittle it all down. It became a process of cue cards on the floor, and of trying to piece it together. I had the idea in Brighton in 2016, developed it there, I have been thinking about it for roughly four years. How long was yours?

LJ: I've been working on it for two years. For me, I do believe that the personal is political, so that fed into it. I'd been working with [performance artist] Diane Torr's pupil Annabel Cooper in creating the Daddy character. It's not only fatherhood though, it's picking apart what a woman is meant to be on stage.

HC-W: Do you think this is the work where you are taking the most risk?

LJ: Yes, it's so important. I have had to look at a lot of dark stuff.

HC-W: I dealt with a lot of trauma, sometimes I live with it onstage, but I do think it's important to deal with it … saying it, pushing it forward.

LJ: Do you feel you've been traumatised by making autobiographical work?

HC-W: There have been points where I'd have to tap out for the day. But I have used it in a way to process it. I think this show is the most exposed I've ever been. I've created ways through the craft of dealing with it. My experience before with the Fringe was with cabaret shows, working with Miss Behave and Briefs, so the crowd are always receptive. Cabaret is designed to get the crowd pumped, with loud music and flashing lights. This will be very different.

LJ: Because I'm based in Scotland, a lot of my friends come to see my work. My previous work, like Hopeless, was more like a gig. A lot of my audience don't come to see theatre, so it'll be interesting to hear what they think.

HC-W: I am so excited to see your show!

LJ: And yours. Can't wait!

Daddy Drag, Summerhall, until 25 Aug (not 12, 19), 5.45pm, £10 (£8).

Sex Education, Summerhall,until 25 Aug (not 12, 19), 7.10pm, £12 (£10).