I agree with cl-r that although “j’ai peur que ça, ce soit ma chaise” is correct when writing, it would not be heard/used orally.
(Some might even argue that “j’ai peur que” would permit/require the “ne expletive” or the "non-negative ne" in formal usage giving: “j’ai peur que ça, ce NE soit ma chaise” to mean the same positive idea [i.e., “I’m afraid that’s my chair], but as an Anglophone my ear is not good at all in recognizing/understanding this weird use of NE, so I’ll try to avoid further mention of it, but I will put it in brackets [NE] in any subjunctive clauses that might follow in case formal use would still require it).
Personally, even in writing, I’d look for ways to avoid “… que ca, ce [NE] soit…,” even to the point of avoiding both “ça” and “ce” completely with:
“j’ai peur qu’elle [NE] soit ma chaise” or, to keep the idea of “ce”:
“j’ai peur que celle-ci (or “celle-la”) [NE] soit ma chaise.”
Orally, you could ignore the subjunctive as cl-r suggests with "J'ai peur que ça, c'est ma chaise," but you could possibly maintain the subjunctive while remaining somewhat informal (and maybe “somewhat” incorrect, but no more so than going without the subjunctive, IMO) with:
“j’ai peur que ça soit ma chaise”
(please note that here, in this informal oral setting, I don’t even propose the [NE] in brackets, but maybe you could use it if you were after the comic effect to which cl-r refers).
Regardless, I appreciate your politeness! In that situation j’ai peur que je [NE] lui dise:
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