No, there is no third sibling in canon.
In literature, Sherlock's only sibling is his brother Mycroft. From the Baker Street Wiki:
Mycroft Holmes appeared or is mentioned in the following adventures:
"The Adventure of the Greek Interpreter"
"The Final Problem"
Adventure of the Empty House" (mentioned)
"The Adventure of the
Sherlockian also discussed this, commenting:
The rest of the family
It is natural to wonder whether there were other brothers in the
Holmes family. None are mentioned in any of the original Sherlock
Holmes tales. But the 1975 film "The Adventure of Sherlock Holmes'
Smarter Brother", starring Gene Wilder, is not about Mycroft; instead,
Wilder presents a manic third brother, Sigi Holmes. Presumably the
name is short for Sigerson, taken from the alias used by Holmes in
"The Empty House".
A number of Sherlockians have ventured to speculate
about a brother named Sherrinford. That name is taken from Arthur
Conan Doyle's original notes for A Study in Scarlet, in which the name
Sherrinford is used for the consulting detective who would shortly
appear in print under the name of Sherlock.
And what about sisters? There is no evidence, apart from a few wistful
comments in "The Copper Beeches" to the effect that "no sister of
mine" should run the risk that faced Violet Hunter.
From this, it can be clearly seen that there is no third brother in canon.
That doesn't mean a third brother won't appear in the show. From many interviews with Steven Moffat:
When we asked how the briefly mentioned third Holmes brother may
eventually play into the series, Moffat, not surprisingly, teased that
we should just, "Wait and see!"