If you’re looking for a free Twitter app that is accessible, check out Twidere for Android by Mariotaku:
https://play.google.com/store/apps/details?id=org.mariotaku.twidere&hl=en
This is a very brief guide to get started.

Immediately after Twidere installs from the Play Store, you’ve got two preliminaries to take care of. First, the app tells you to log into Twitter. Just tap OK or Continue to launch your browser, enter your Twitter user name and password, and tap the sign in button. Second, the app brings up a series of settings screens. Tap Next to move through them, making changes if you have convictions or leaving things as they are if you don’t. At the end of this process, you may be asked to allow location and one or two other things.

The Twidere main screen is pretty simple. Across the top are four tabs: Home, Interactions (i.e., Mentions), Trends, and Messages (i.e., Direct Messages). In the bottom right corner is a New Tweet icon. The first time you visit a tab, the screen displays no tweets or messages; you need to refresh to populate the screen.

To visit a tab, either tap the tab icon at the top of the screen, or swipe left or right with two fingers. For example, let’s say you’re on your timeline and you want to go to your mentions. Either tap Interactions, or swipe left once with two fingers.

To refresh the screen, long-press its tab icon. For example, if you want new tweets to appear, long-press Home.

To open the menu, touch the very left edge of the screen, then swipe right with two fingers. This is one of those things that takes a little practice, then works right every time.

Once tweets are displayed on the screen, each has three lines of information. The top line is the sender’s name and Twitter handle. The middle line is the sender’s profile icon and the tweet itself. The bottom line is a row of controls, which varies a little. Typically, controls are Reply, Retweet, Like, and an unlabeled button I’ve called More. Tapping More brings up additional controls, like Share, Copy, and Add to Filter. Exploring is the best way to read the screen.

To send a new tweet, tap the Compose icon in the bottom right corner. The new screen displays an edit box (above) and the keyboard (below). To the right of the edit box are a check box for adding your location and the Send button. Below the edit box is a row of icons for changing the account, adding an image, taking a photo, and saving as draft.

The app is very accessible. The only hiccups I’ve found are the unlabeled button in the third row of each tweet and the fact that TalkBack doesn’t announce, “Selected,” when you touch the tab for the screen you’re on.