Have you seen the memes that go like this?
A pastor friend just mentioned something that I had also wondered, that the figure 365 seemed high! So I ran it through my Bible software, and within a few minutes found that the number indeed was way, way off.
“Fear not” is a Kings-James-ism; the NET and the NASB versions each have it a few times, the other modern versions do not, including the New KJV; the earlier English versions do use it: Douay-Rheims, Coverdale Bible, Geneva Bible. So, checking the KJV, I would say that are exactly 70 examples of the phrase “fear not.” But only around 44 are in the sense of, “Fear not, because God is with you,” as said by God or some messenger. The other 26 examples are more mundane: “Fear not [Rachel], your baby [Benjamin] is almost born” (Gen 35:17) and other things.
33 “fear nots” are from the Old Testament, 11 from the New Testament; Isaiah is the winner with eight instances; taken together, the Nativity stories of Matthew and Luke have four.
#1 is this well-known verse: “Fear not, Abram: I am thy shield, and thy exceeding great reward.” Gen 15:1
#44, the last, is Rev 1:17 – “And he laid his right hand upon me, saying unto me, Fear not; I am the first and the last.”
Even if one expanded the search to include other versions of the phrase (“do not be afraid,” for example), one does not attain the magic number of 365.
That is to say, the Bible has 365 “Fear not” passages if and only if you own nine copies of the King James Bible.
Of course, if one wanted to say that there are hundreds of verses which, whether they use the specific phrase “fear not” or not, serve to allay our fears with God’s promises, they will get no argument from me! To begin with, Matt 6:34 – “do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.” My point here is not to be finicky with regard to the semantics, but rather that, (1) it’s too easy to pass along “facts” without checking them, and (2) that preachers especially, more than are the laity, are under an obligation to check the facts before repeating them.
PS – To mention another “fact”: I have lately seen “Prophecy Experts” claiming that unless the United States backs the permanent unification of Jerusalem and the expulsion of the Palestinians, then they will fall under God’s final judgment. This is based on “… there will I deal with and execute judgment upon them for their treatment of My people and of My heritage Israel, whom they have scattered among the nations and because they have divided My land” (Joel 3:2). In my opinion this is a poor interpretation indeed of the Joel passage; but my point here, again, is that the preacher who hears this being passed around is under obligation to determine for him/herself whether this really means that Jerusalem must be the capital of the modern State of Israel and not (simultaneously) the capital of a Palestinian state.
 Here is one example among many: https://www.christianpost.com/news/rick-warren-why-god-encourages-christians-to-fear-not-365-times-in-the-bible-163029/
 Here is the list of 44: Genesis 15:1, 21:17, 26:24, 46:3, Exod 20:20, Deut 1:21, 20:3, 31:6, 31:8, Josh 8:1, 10:25, Judges 6:23, Ruth 3:11, 1 Sam 12:20, 22:23, 2 Kings 6:16, 1 Chron 28:20, 2 Chron 20:17, Psalm 78:53, Isaiah 7:4, 35:4, 41:13, 41:14, 43:1, 43:5, 44:2, 54:4, Jeremiah 46:27, Lamentations 3:57, Daniel 10:12, Daniel 10:19, Joel 2:21, Zech 8:13, Matthew 1:20, 28:5, Luke 1:13, 1:30, 2:10, 5:10, 8:50, 12:7, John 12:15, Acts 27:24, Revelation 1:17. The verse mentioned in the second meme, Joshua 1:9, has “fear not” only in the older Catholic Bible, the Douay-Rheims.
 Here is one of the most extreme versions of this idea (the site gleefully approves of keeping Palestinians surrounded by security fences, making it easier for their complete annihilation when the time is right). Many prophecy pundits take the same view of these key Old Testament passages, but not approving of genocide. See eg, David Jeremiah.
“Preachers: don’t believe everything you hear!” by Gary S. Shogren, Professor of New Testament, Seminario ESEPA, San José, Costa Rica