The word “paradise” signifies “a delightful garden, park or pleasure ground.” The Garden of Eden was the original paradise, where man dwelt before disobeying the Divine command. Because of disobedience, he lost this paradise (Genesis 3:22-24).

When the race of mankind again comes into harmony with the Creator by becoming obedient to the Lord, after they are raised from the dead and have the opportunity to learn about righteousness, the earth will become like the Garden of Eden, and mankind will be restored to that Edenic condition (Acts 3:19-21; Ezekiel 36:35). “The desert shall bloom and blossom as the rose and springs shall break forth in the wilderness, and the solitary place shall be glad for them” – the happy world of mankind (Isaiah 35). Such conditions will take place when our Lord “comes into his kingdom.” 

The thief asked to be remembered “when thou comest into thy kingdom,” and our Lord will come into his kingdom at his return. Our Lord did not go to paradise that day, but went to the tomb/the grave, from which he was raised the third day. 

The passage with the punctuation properly made, placing the comma after the word “today,” clears the matter up. “Verily I say unto thee today (now), thou shalt be with me in Paradise” – at my return, when the kingdom of heaven shall be established in the earth. Punctuation is a modern invention, dating from the year 1515 A.D. The comma was placed in the text by the translators under King James, and it is evident that they made the mistake of placing it before instead of after “today.”

Additional Resource:
Christian Questions Podcast
Episode #988: “Did Jesus and the Thief Go from the Cross to Paradise?”
Finding the true meaning of Jesus’ words to a thief about paradise
CQ Rewind Show Notes