I created a world that's axial tilt is on a constant 45 degree angle in the northern hemisphere it would look something like this. The problem is I can't figure out how the wind currents would work.
the planet has the same mass, size, orbit speed and rotation speed as earth. If anyone can explain it to me it would be a big help.

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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Sep 20 '22 at 03:30
2 Answers
It won't work the way you want it to
There is a fundamental error in your assumptions. You have your world inclined 45 degrees, fine - but its axis of rotation will not change when it orbits the sun. If one hemisphere has midnight sun during its summer, it will have 24/7 darkness during its winter.
To have something like what you want, you need to have the planet tidally locked to the sun, with the same side always facing it, the way that our moon always shows the same side to the Earth. In other words, its rotates once a year. You can't have both rotation speed and orbital speed like the Earth's, like you ask for.
Studies have been made about the climate on tidally locked planets. You can access two of them here and here.
Also check the answer to this earlier, similar question.

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Almost an Eyeball Earth
An Eyeball Earth is a hypothetical type of planet where one side constantly faces the star. There are theories about how the climate would work, mostly on how there are persistent winds between the two sides.
Specifically, the colder, denser air would move closer to the ground, get into the "eye", become warm air, rise up, and then move to the cold side higher up in the atmosphere. I would expect something similar on this planet.
Similar is Not the Same
Ignoring the effects of terrain and ocean currents, both of which are pretty important to climate models, you essentially have a "tropics" ring at very high latitudes. Storms would gain energy there, move to the cold side, and cause rain/snow as they cool off. I would expect something like Hadley Cells to form, but built around the "tropics ring" instead of the equator.
Additionally, since the planet is also rotating, you get Coriolis effects on these storm systems. It wouldn't be a straight shot over to the cold side: everything would drift and spin. This would cause interesting variations in weather patterns.
Inside the Tropics
Additionally, the area inside the "tropics", the cap formed by the ring where the sun is directly overhead, would be very interesting! It would have near constant exposure to the sun and be on the tail end of cold air systems. Surface winds would likely be calm, like the doldrums on earth. There could possibly be a desert or very warm sea there!

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