Image source: Getty Images As a veteran investor with over 35 years’ experience of buying shares, I frequently scan the FTSE 100 and FTSE 250 indices for cheap shares. In a recent stock screen, I found more than 20 Footsie shares paying high yields (for me, defined as at least 5% a year). Shares I own for juicy dividends Since mid-2022, my wife and I have been building a new share portfolio. Our main goal with this new asset is to generate high levels of income. We can then use this extra cash to help pay our soaring bills, or reinvest in more shares. So far, we’ve bought 17 new stocks, with at least three more purchases to come. Meanwhile, here are three cheap ones we bought for their excellent dividend-generating properties: CompanyLegal & GeneralRio TintoVodafoneBusinessFinancial servicesMiningTelecomsShare price260.8p6,291p93.42p52-week high295.7p6,406p141.6p52-week low201.4p4,424.5p83.24p12-month change-10.0%+13.0%-25.9%Market value£15.6bn£105.7bn£25.4bnPrice-to-earnings ratio7.77.214.6Earnings yield13.0%13.9%6.8%Dividend yield7.2%8.3%8.4%Dividend cover1.81.70.8 These three come from very different corporate worlds. Legal & General Group is one of the UK’s leading providers of life assurance, savings and investments. Anglo-Australian miner Rio Tinto is one of the globe’s biggest producers of aluminium, copper, iron ore and zinc. And telecoms giant Vodafone is a world-leading provider of mobile and broadband services. When building a portfolio, this stock diversification — spreading money across widely differing companies and sectors — is a very good thing. It helps to prevent concentration risk and avoids having too many eggs in similar baskets. These three shares offer market-beating cash yields The next thing I’d say is that all three have low or modest price-to-earnings ratios and high earnings yields. For me, this is the definition of a ‘cheap’ share — one with an earnings yield that beats the market average. Legal & General and Rio Tinto have earnings yields of 13% and nearly 14% respectively — roughly double the FTSE 100’s under 7%. But what drew us to buy these stocks for our family portfolio is their market-beating dividend yields. The highest (8.4% a year) comes from Vodafone, whose share price has crashed more than a quarter over the past 12 months. However, this cash yield is covered only 0.8 times by earnings, making it the least solid of this trio’s payouts. Conversely, at Rio Tinto, the dividend yield of 8.3% — over twice the FTSE 100’s cash yield — is covered 1.7 times by earnings. Although history has taught me that mining dividends can be very volatile, I’m currently confident in Rio’s 2023 payout. Then again, Rio last cancelled its dividend in 2016. Oops. Lastly, L&G’s cash yield of 7.2% a year has the highest dividend cover, at 1.8 times. I consider this payment to be rock-solid — barring another market meltdown, that is. Indeed, I’m looking forward to owning this share for many years for its income-generating ability. In summary, we bought these three cheap shares after their prices fell steeply. And now we intend to hold them for passive income for many years — or perhaps until their dividends get cut!