Capsicum is a very kind pursued by these pests. They are very common, aphids and white flies. Not much to do, but you can spray with soapy water with white soap, and manually clean their leaves. There are also systemic insecticides, but they are very toxic. 

Thank you @Prof. Scaldaferro.

I am read your discerption but I needs same information like photos than defiantly I will help you and I think this is mealy bug insect according your discerption but I am not sure so your spray insecticide Imidacloprid 0.35 g/litre of water for the control of mealy bug insect.   

Dear Ajay,

It seems that your problem is aphids. You can try to find natural ennemies, like coccinellidae or chrysopidae

https://fr.wikipedia.org/wiki/Chrysopidae#/media/File:Chrysoperla_carnea_larva02.jpg

You have problems with black aphids and white flies.

Many of the insecticides used to control other pepper insect pests can contribute to rapid increases of aphids and whiteflies. Natural enemies such as lady beetles, parasitoids (Aphidus, Aphelinus, Encarsia, Amitus etc) green lacewings, damsel bugs, and hover fly larvae usually control aphids and whitefly populations adequately. Broad spectrum insecticides, particularly pyrethroid insecticides, can delete these natural enemies and allow aphid populations to develop unchecked. Insecticides should only be applied for other insects when necessary, as determined by trap catches and scouting, and care should be taken to select insecticides that do not favor secondary aphid problems. 

Dear Ajay Kumar

 The insects as  mentioned aphids and white flies , If the plant in pots, and you don't want to use insecticides you may hold it and immerse the upper parts in a soap/water path for 3 min. Then washed it with water then day by day try to brush out the aphid, good luck

Hoping this will be helpful

Regards

Prof. Houda Kawas

Your plants are infested by aphids. You need insecicide treatment.

Based on your description of a "white powdery mass" I would agree with Deepak Kushwaha, that the pest is likely mealy bugs. Wooly aphids and wooly white flies are also possibilities. Mealy bugs will be sticky and cottony if you try to remove them, often found on stems. Only the larvae are very mobile. Wooly aphids are more likely to be actively moving around. Wooly aphids and wooly white flies are more often found on leaves than mealy bugs. I also agree that you should not spray any insecticides until you have a positive identification.  I recommend comparing your insects to the following pictures:

https://uofacesmg.wordpress.com/2015/06/17/woolly-aphids-versus-mealy-bugs/

http://ipm.ucanr.edu/PMG/GARDEN/PLANTS/INVERT/mealybugs.html

http://ipm.ucanr.edu/PMG/GARDEN/PLANTS/INVERT/woolaphids.html

https://cals.arizona.edu/crop/citrus/insects/woolywhitefly.pdf

It may help to look at the insect under a microscope and/or post pictures here for the group to look at. If you have access to a plant disease and insect diagnostic clinic, they are a good resource. You could also ask someone from your entomology department at the university.

thanks to agree with my answer

Dear Dr. Deepak Kushwaha, Prof. Pierre Huguier, Prof. Luis Miguel Constantino, Prof. Houda Kawas, Dr. Melissa Irizarry.

Thank you for your kind replies and remedial measure.

Regards

you most welcome

Houda

Your pictures very clearly document an aphid infestation (probably a species in the Aphis fabae complex). However, aphids are in turn heavily infested by an entomopathogenic fungus (the white mold sticking dead individuals on the leaf surface), which you can eventually try to isolate and identify at the genus level through the microscope based on its conidial structures. I think that this fungus will completely defeat the aphid later on, and it would be really interesting if you can confirm this hypothesis by avoiding the use of insecticides, at least on some plants. Please let me know what happened, in case you are following my suggestion.

This is the Aphid infestation

and white powdery mass is exuviae (skin) of aphid.

Several polyphagous aphid species, such as Myzus persicae Sulzer, Macrosiphum euphorbiae (Thomas), Aphis gossypii Glover and Aulacorthum solani (Kaltenbach).

Among these different insect-pests attacking sweet pepper, M. persicae is the most serious.

Application of Cohigan 17.8 SL@ 1ml/l or Aktara or 7-Star 25 WG @1 g/3 liter of water or Polar 20SP @0.5g/l  should be apply. Two applications of foliar sprays, a week apart, are often needed.

Dear All,

There must be two aphid species on the showed paprika plants. One of them may be Aphis fabae and the other is perhaps a green aphid which cannot be properly seen (on the picture 4). No whiteflies can be observed. Rosario may be right, A. fabae must be infected by entomopathogen fungi. Against aphids in low density you can apply horticultural oils or soaps if the fungi present will not control them.  

You have problem with aphid species.

Hi: This is just aphids

Purely aphids, well fed ones. Rosario has an idea about the issue with entomopathogenic fungi you can maybe sample few plants then spray the rest with Thiamethoxam(Actara) and your problem will be sorted.