VBA copy cells value and format
Instead of setting the value directly you can try using copy/paste, so instead of:
Worksheets(2).Cells(a, 15) = Worksheets(1).Cells(i, 3).Value
Try this:
Worksheets(1).Cells(i, 3).Copy
Worksheets(2).Cells(a, 15).PasteSpecial Paste:=xlPasteFormats
Worksheets(2).Cells(a, 15).PasteSpecial Paste:=xlPasteValues
To just set the font to bold you can keep your existing assignment and add this:
If Worksheets(1).Cells(i, 3).Font.Bold = True Then
Worksheets(2).Cells(a, 15).Font.Bold = True
End If
This page from Microsoft's Excel VBA documentation helped me: https://docs.microsoft.com/en-us/office/vba/api/excel.xlpastetype
It gives a bunch of options to customize how you paste. For instance, you could xlPasteAll (probably what you're looking for), or xlPasteAllUsingSourceTheme, or even xlPasteAllExceptBorders.