If I apply for EB1C category, does my dependents also have to be with me while applying?

Your family can apply for their visas in your home country to join you.

Your dependents will be able to apply for an immigrant visa at the US Embassy in their home country once your I-140 is approved as EB1.

If they are named in your petition, if you get a green card, CIS will give your wife and children under 21 years the same consideration by allowing them to "follow to join" you in the US as green card holders themselves by consular processing from their country.

Your employer will be applying for immigrant visas - for you and for the members of your family who can, by law, receive a derivative immigrant status by virtue of being related to you. Neither you, nor your relatives have to be in the U.S. for filing of the applications. Since you are in the U.S., your employer's petition should be filed together with your application for adjustment of status; you will not need to leave the U.S. to obtain a green card. If your family members are abroad, they will go through the consular processing: after approval of your employer's petition, USCIS will forward the case to National Visa Center of the Department of State, which, in turn, will send it to the U.S. Embassy in your country of citizenship; the U.S. consul will invite your wife (and, possibly, children) for an interview and issue immigrant visas that would allow them to come to the U.S. and receive green cards. Your family will have a year to join you in the U.S.; if necessary, this time can be extended.

You must file a petition to have them join you with in 6 months after you obtain the Green Card Fakhrudeen Hussain Attorney At Law Immigration.