A plumber just changed the hardware inside the toilet. But now when I flush it seems that the water starts to go down and stops. You have to hold the handle down to get a full flush.
When I called the plumber he said its because these new toilets don't hold as much water as the old one, but he won't come back to fix it saying its to small of a job. How can IO fix this.

Do not fix it. You had a working toilet and the plumber fixed it and now you do not have a working toilet. In the united states we have something called the bbb, better business bureau. Calling them gets a response from your plumber quickly because they can hurt his business if he is not doing right. Make the plumber fix it.
However, if you do not want to deal with him again, then your problem is likely low water level in the tank. Or a water saver flapper. Or an improper installation of the flapper. I personally set the water level in the tank as high as I can without letting it leak from the handle. This would be about 1/4" from the top of the overflow. What does your fill valve look like? This is the valve that lets water enter the tank. Next would be the water saver flapper. It usually either has an additional float on it or a hole in the side of the flapper. Change it to an older style cheap flapper. It typically has a ring to slide down the overflow and ears to hook on the catches at the bottom of the overflow. Use one method or the other, not both. Most people cut the ring off. By the way, what brand of toilet? One piece or 2 piece?

Check the tank water level, it should be at the mark in the tank or 3/8 to 1/2" below the top of the over flow tube. Now look at the flapper, If it has wavey edges on the flat surface, replace it. The linkage between the flapper and the flush lever should have 1/4" play when the tank is filled. Also, check the small tube coming out of the top of the bakkcock and make sure it's connect to and draining into the white overflow tube. Regards, Tom

New toilets flush better with less water than the old ones which use up to 3 gals. Of water. Your plumber did not do a good job and it is unfortunate that he has his money and is not willing to fix your problem. Speedball has given you all the right recommendations. Doug 238 has the right idea about filing a complaint. Don't accept this laying down.