You can not get a habitable planet with Earth like temperatures orbiting a star with a mass equal to the Sun with an orbital period or year one Earth day long. Thus you will have to settle for a star a lot different from the Sun for an Earth like planet to have a year one Earth day long.
The mass of a star (and its age to a lesser degree) will determine how much radiation the star will emit. The amount of a radiation a star emits will determine the distances of its habitable zone where a planet could orbit and have Earth like temperatures. The mass of the star and the orbital distance of the planet determine the planet's orbital speed and the length of its year.
There are known exoplanets with years less than one Earth day long. But they are not orbiting in the habitable zones of stars with masses equal to that of the Sun.
There are exoplanets known to orbit in the habitable zones of their stars, making those exoplanets potentially habitable exoplanets.
Their year lengths vary widely. The four planets in the habitable zone of TRAPPIST-1 included the three potentially habitable exoplanets with the shortest known days; 9.2 days, 6.1 days, and 4.05 Earth Days.
I haven't done calculations, but I think it is possible for a planet in the habitable zone of a star to have a year as short as one Earth day.
But all the potentially habitable worlds orbiting in the habitable zones that have very short years orbit around very dim red dwarfs of spectral class M. And those stars are much less massive than the Sun.
For a planet to orbit in the habitable zone of its star with a year one Earth day long, it would have to orbit around a class M star even dimmer than TRAPPIST-1 even closer than TRAPPIST-1d does. So there would seem to be absolutely no possible way for that star to have the same mass as the Sun.
It has been calculated that planets orbiting in the habitable zone of a red dwarf star would become tidally locked to their stars, with one side constantly facing the star and having eternal day and one side constantly facing away from the star and having eternal night. And it is controversial whether a planet could be Earth like and habitable if it was tidally locked to its star.
One way out of that problem would be to have the Earth-like planet actually be an Earth like giant moon of a giant planet. The moon would orbit the planet which would orbit the star. The Moon would become tidally locked to the planet and not to the star, and so it would have a daily cycle of light and dark equal to the period of its orbit around the planet.
If you try that, it would be more likely for the Earth like moon to have an orbital period of one Earth day around the planet, and for the planet to have an orbital period of at least several days around the star, instead of the planet having an orbital period of one Earth day around the star, and the moon having an orbital period of a fraction of an Earth day around the planet. So that would not be exactly what you want.
Of course it is always possible, depending on various theories about the subject, that a tidally locked planet orbiting close to a red dwarf star could remain habitable.
Since Trappist-1 is spectral class M8V a habitable and Earth like planet with a year one Earth day long would probably be class M9V, or even dimmer.
If a red dwarf with spectral class M9V would still be too luminous to have a Earth-like planet with a year one Earth day long, you would have a problem selecting an even dimmer type of star.
You might need to go with a white dwarf star. White dwarf stars are much hotter than red dwarf stars, so each area of their surface emits a lot more radiation than the same area of a red dwarf star does. But white dwarfs can be very small, and so can have a lot less surface to emit radiation from.
Thus the dimmest white dwarf stars might be a lot dimmer than the dimmest red dwarf stars.
White dwarf stars, despite their smaller sizes, are also very dense and so are more massive than red dwarf stars. Thus a planet orbiting a white dwarf star might have to orbit faster to stay in orbit, and have a shorter year, than it would have if it orbited a red dwarf star at the same distance.
So white dwarf stars would be a good choice for an Earth like planet with a year on e earth day long. Except for the history of white dwarf stars.
White dwarf stars were once massive stars which had to burn their fuel very quickly, and so have run out of hydrogen to fuse, expanded into red giants, and then shrunk down to tiny white dwarfs shining with leftover heat.
That process would have destroyed any planet orbiting that close. So the Earth like planet would have had to have been moved from someplace else into its present orbit by rather unlikely natural forces or by a highly advanced civilization, and then remained in its new orbit for billions of years while it gradually developed Earth like conditions on its surface.
another possibility would be to have the planet orbit around a brown dwarf. A brown dwarf is an object more massive than a planet and less massive than a star, that would mostly emit invisible infrared radiation. A planet orbiting a brown dwarf of the right mass and luminosity might possibly have a year one Earth day long while orbiting within the habitable zone of the brown dwarf, though I haven't made any calculations.
So there are several possibilities for someone to calculate an orbit within the habitable zone with a length of one Earth day.
One) a red dwarf, probably spectral class M9V.
Two) a white dwarf, where the planet has been moved into its present orbit billions of years ago, after the star became a white dwarf.
Three) a brown dwarf.