3:15a

You killed: Roman soldiers killed Jesus. But the Jews demanded that they kill him. Pilate accepted their demand even though he disagreed with it. So the Jews were most responsible for killing Jesus. In some languages a literal translation would indicate that the Jews killed Jesus themselves. If that is true in your language, indicate that they caused his death. For example:

You had the author of life killed

the Author of life: There are three ways to interpret the Greek word that the Berean Standard Bible translates as Author here:

(1) It means author/originator. For example:

the author of life (New Living Translation (2004))

(Berean Standard Bible, English Standard Version, New International Version, Revised Standard Version, New Living Translation (2004), NET Bible, New American Bible, Revised Edition, God’s Word, New Century Version)

(2) It means prince. For example:

the prince of life (New Jerusalem Bible)

(King James Version, New American Standard Bible, Revised English Bible, New Jerusalem Bible)

(3) It means leader. For example:

the one who leads to life (Good News Translation)

(Good News Translation, Contemporary English Version)

It is recommended that you follow interpretation (1).

Here the phrase the Author of life probably indicates that Jesus causes people to live. It may also imply that the people who believe in him will live with God eternally. Here are some other ways to translate this phrase:

the Originator of life (NET Bible)
-or-
the source of life (God’s Word)
-or-
the one who gives life

3:15b

but God raised Him from the dead: The Greek is literally “whom God raised.” But there is implied contrast here, so the Berean Standard Bible translates the contrast with the word but.

God raised Him from the dead: This clause indicates that God caused Jesus to live again after he had died. Here are some other ways to translate this clause:

God brought him back to life (God’s Word)
-or-
God made him live again

3:15c

we are witnesses of the fact: The word witnesses refers to people who tell others what they themselves have personally seen and heard. In some languages a phrase with a verb is used. For example:

we(excl) can testify to this
-or-
we…have seen with our eyes [emphatic] that he lives again

See how you translated witnesses in 2:32b.

we: Here this pronoun refers to Peter and John.

the fact: The phrase the fact refers to God raising Jesus from the dead (3:15b). Here are some other ways to translate this word:

this/that
-or-
that he ⌊truly⌋ came alive

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