Aerospike nose cones for supersonic jets?
There are no historical aircraft with an aerospike nose, at least, none that I remember, and none that I could find after 30 mins of research. I'm not sure if there are any planned projects using it, but I doubt there are, given the purpose of aerospike noses - aerospike noses really only have one main purpose - to streamline a blunt body. This is commonly used in missiles and such (especially in SLBMs), where height/length is a constraint - a slender, sharp nose is very long, so to save height, those missiles are fitted with an aerospike that telescopes out. The flat plate at the end of the aerospace forms a detached bow shock, which makes the airflow "see" the blunt body as having a different, more streamlined shape, reducing drag. Here's a visual of that happening:



Image source - https://iopscience.iop.org/article/10.1088/1742-6596/1276/1/012031/pdf

However, the bow shock generated by a drag reducing aerospike causes more drag and a heating than the oblique shock generated by a slender nose of the same length. For SLBMs, a long, sharp nose is obviously out of question (well, you could have a telescoping sharp nose, but that would be heavy), but for aircraft, length really isn't a concern, you can make the nose as long as needed. Therefore, it doesn't really makes sense for an aircraft to have an aerospike nose.