How can I set the right font of heatmap to be italic?And some font to be superscripts or subscript below heatmap?

You can use plotmath expressions in the labels:

library(pheatmap)

rmt <- matrix(rnorm(9), ncol = 3)

pheatmap(rmt,
         labels_row = c(expression(italic(Aaaa)), expression(B^b), expression(C[c])),
         labels_col = c("E","F","G"))

Created on 2024-02-01 with reprex v2.0.2