I am looking for an eSignature API for my website which is also economical.
The digital signature API can be purchased from DocuSign, Hellosign and various other eSignature tools. Based on your document and signature request, the API can be purchased. I personally find DigiSigner a good solution with minimum cost. Hellosign APIs plans are quite expensive and I havent tried DocuSign as of yet, so cant comment on its productivity. On the other hand, DigiSigners API plans quite economical and are listed here. In Plan 300, you get 300 documents support and as far the API integration is concerned, there are prebuilt PHP and Java client libraries to make the integration process even easier. You can also use custom branding on the DigiSigner signature page and in the DigiSigner emails.
Also, DocuSign API pricing is listed here.