Fake tweets are observed to be ever-increasing, demanding immediate countermeasures to combat their spread. During COVID-19, tweets with misinformation should be flagged and neutralized in their early stages to mitigate the damages. Most of the existing methods for early detection of fake news assume to have enough propagation information for large labeled tweets -- which may not be an ideal setting for cases like COVID-19 where both aspects are largely absent. In this work, we present ENDEMIC, a novel early detection model which leverages exogenous and endogenous signals related to tweets, while learning on limited labeled data. We first develop a novel dataset, called CTF for early COVID-19 Twitter fake news, with additional behavioral test sets to validate early detection. We build a heterogeneous graph with follower-followee, user-tweet, and tweet-retweet connections and train a graph embedding model to aggregate propagation information. Graph embeddings and contextual features constitute endogenous, while time-relative web-scraped information constitutes exogenous signals. ENDEMIC is trained in a semi-supervised fashion, overcoming the challenge of limited labeled data. We propose a co-attention mechanism to fuse signal representations optimally. Experimental results on ECTF, PolitiFact, and GossipCop show that ENDEMIC is highly reliable in detecting early fake tweets, outperforming nine state-of-the-art methods significantly.