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I don't think it is Joseph Rogers - that doesn't look like an asterisk on the left and the letters appear to be (probably) H I or I H the other way up. I don't have any other suggestions though.
I think it is 'IH'. John Harrison of Sheffield was known to use the Gothic letters 'I' and 'H' and in their early marks they also included a Maltese Cross.
Not sure what to make of the final mark, to me, it looks like a Mitre?