Count panel models for endogenous regressors
Windmeijer (2000, Economics Letters) presents a treatment of the estimation of count-data models with fixed effects and endogeneity. 

http://www.sciencedirect.com/science/article/pii/S0165176500002287

See this slideshow by Wooldridge for a pedagogic and progressive presentation of panel data models with endogeneity. Count-data models are introduced slide 54. He clearly explains the possible solutions and relate the count-data case to other nonlinear models. 

http://www.ifs.org.uk/docs/wooldridge%20session%204.pdf