𝓞 is extant here and reads “at this period of time”. But when Oliver Cowdery copied the text from 𝓞 into 𝓟, he seems to have initially written “at this time of time”, an obvious error. Later, probably when he proofed 𝓟 against 𝓞, he caught his error, crossed out the first time, and supralinearly wrote period. The ink level for period is somewhat heavier, but the entire inline phrase “at this time of time” shows no change in the level of ink flow.
Elsewhere the text strongly prefers the shorter phrase “at this time”. There are 34 instances of this phrase, including two in Alma 53 that shortly precede the one here in verse 19:
It was perhaps these two nearby instances of “at this time” that influenced Oliver Cowdery to miswrite “at this time of time” in 𝓟.
There is independent evidence for the phraseology “at this period of time”, with three examples elsewhere in the text:
For each case of “at this (period of) time”, the critical text will follow the earliest textual sources. Here in Alma 53:19, 𝓞 is extant and reads “at this period of time”.
Summary: Maintain the relatively infrequent phrase “at this period of time”, found in Alma 53:19 and three other places in the text; normally the text uses the shorter “at this time”.