The following advice and newspaper item came from Katy Bodenhorn Genealogy on Facebook:

In the 1800s, Mc- surnames were often spelled and printed with an apostrophe instead. This could affect your results if you’re making your searches only with Mc or Mac. Use those wildcards (* and ?)

And while we’re at it, you may need to search manually, page-by-page instead of relying on the search bar. In this exact case, the OCR technology didn’t read “M’ilvain” when I queried, and it doesn’t appear in searches. But she’s definitely there.

(Example pictured from the marriages section of the Village Herald newspaper of Woodbury, New Jersey, 28 January 1824.)

Fascinating! I'm particularly interested because of my 3X great-grandmother, Elizabeth McIlveen. Here's some background info provided by Claude.com:

Historical records concerning Irish and Scottish names reveal that the common prefix Mc and the less common prefix M' both developed as abbreviations of the original Gaelic prefix Mac. So M', Mc, and Mac are all orthographically equivalent — none carries a different meaning or cultural signal. M' is now nearly obsolete but was once widely used, and all three forms — Mac, Mc, and M' — are interchangeable and carry no grammatical or cultural distinction...

It was genuinely widespread in the 17th, 18th, and early 19th centuries — not a rare curiosity. You encounter it constantly in:

• Scottish Kirk session records and parish registers
• Ulster Plantation-era land and muster rolls
• American colonial and early republic documents (especially in Pennsylvania, Virginia, and the Carolinas, which received heavy Scots-Irish settlement)
• Printed city directories of the 1700s and early 1800s
• Wills, deeds, and court records across the British Isles and their colonies