Answer: This is a very difficult location to plant, as it is probably dry, exposed to the northwest wind in winter and also has hot afternoon-only sun. You might be able to grow a juniper there, or possibly a mugo pine, or possibly a yew. You may need to water it during months the ground is not frozen, if the overhang prevents rain from reaching the roots. I would suggest you work with your local county extension and professionally trained nursery staff to try to identify plants that might thrive there, and then select one of those. They should be able to make less tentative suggestions based on a more detailed understanding of the planting site and your overall design goals. Good luck with your evergreen!
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