I live at 6035 ft. I always have to 'altitude' my baking. What I would suggest is reduce the sugar by about 1-2 TBSP. Because it turns to a liquid when heated and then evaporates. Increase flour by about 2 TBSP. You are strengthening the batter, to allow for lack of air pressure. Reduce any baking soda or baking powder by about 1/8 tsp. Preheat your oven to 25 degrees hotter than what is required. Then lower the temp to what is required just as you put them in.
It's difficult to say without seeing the recipe, but my go to method for keeping cakes moist (and keeping them from falling) is adding an extra egg. I'm at about 5500 ft. Given that this recipe is supposed to make so few cupcakes I might only add a yolk, rather than the whole egg.
What sort of changes you need to make will really depend on your altitude- because even those vary depending on exactly how high you are. The best way to start would be to read over the info at King Arthur - https://www.kingarthurflour.com/learn/high-altitude-baking.html High altitude baking can be a bit tricky, and take some time to figure out the best methods to work in your particular setting. So keep notes about what you try and how it works, what the results are like. From that you can fine tune your adjustments, not only for your altitude, but your oven and you. Good luck!
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What I would suggest is reduce the sugar by about 1-2 TBSP. Because it turns to a liquid when heated and then evaporates. Increase flour by about 2 TBSP. You are strengthening the batter, to allow for lack of air pressure. Reduce any baking soda or baking powder by about 1/8 tsp. Preheat your oven to 25 degrees hotter than what is required. Then lower the temp to what is required just as you put them in.
https://www.kingarthurflour.com/learn/high-altitude-baking.html
High altitude baking can be a bit tricky, and take some time to figure out the best methods to work in your particular setting. So keep notes about what you try and how it works, what the results are like. From that you can fine tune your adjustments, not only for your altitude, but your oven and you. Good luck!