This is really more of a question for Astronomy.SE, in general this doesn't happen, but circumstances can work out that it does, see the updated last few paragraphs.
Every meteor shower with an identified cometary source comes from a comet with a period longer than one year, but the meteor showers are still annual. The Eta Aquarids and the Orionids are sourced from Halley's Comet, and it has a period of 75-76 years.
The debris and dust shed by the comet as it orbits (at least, that part of it ejected fast enough to escape the comet's meager gravity) winds up in an orbit around the Sun; generally an orbit close to the comet's orbit, maybe a little smaller, maybe a little larger, maybe a tiny bit off-inclination. The result is an orbiting swarm of dust, gas and debris surrounding the orbit of the comet, and when the Earth passes through the area of this elliptical torus, that's when some of it passes close enough to hit the atmosphere, and we see meteor showers.
That said, the meteor showers themselves are typically more significant when a passage of the generator comet is recent.
And credit to Mark, there are meteor showers that do exhibit the requested behavior. Comet 55P/Tempel-Tuttle is the source of the Leonid meteorite shower, and it has an orbit that gets under 1.5 million kilometers from Earth's orbit. As a result, the recently-shed dust and gas doesn't have to disperse far from the comet's orbit to encounter Earth. So with most comets as this dust spreads out, the individual effects of each perhelion passage are lost in the noise, but with the Leonids and Tempel-Tuttle, the nearness of the passage means that the perihelion density clumps are better defined when Earth encounters them, resulting in a spectacular jump in meteorite frequency a bit over every 33 years (the orbital period of the comet), with a far higher proportion of meteorites than usual.
The last such peak were the 1999-2001 storms. 2022 is predicted to produce a higher-than-average level, but not meteor-storm level.
Given a similar setup, it's not hard to imagine a situation where the peak every 50 years on a hypothetical 50-year comet gets noticed by everyone in a fantasy setting, but only those who really know their astronomy notice that a lesser version happens every year. Especially if the last few times it happened, things kicked up into the dozens of thousands of meteors per hour range.