The most commonly recommended abbreviation for “continued” is cont. Cont'd is also a correct way to make “continued” shorter. It's a contraction, rather than an abbreviation. When writing continued on next page you should consider spelling out the full phrase instead of using a shortened form.

What does contd mean in a script?

CONT'D (an abbreviation for continued) should be written next to the character's name to indicate that their speech is continued.

How a script is written?

When script writing, your script, also known as a screenplay, should detail character dialogue, scene settings, and actions that take place throughout a film, TV show, or another visual story.